Ace: People often use those words interchangeably, but yes there's a big difference!
When a character is described as asexual in fiction it's usually used as a shorthand for "aromantic asexual". A character who is asexual, and thus lacks an interest in sex, almost always also lacks an interest in any romance at all. This, however, is a simplified version of asexuality that isn't accurate to reality.
In real life, asexuals come in a variety of "romantic orientations" ranging from "heteroromantic" (romantically attracted exclusively to the opposite gender) and "panromantic" (romantically attracted to all genders), while "aromantic" (romantically attracted to no one) is only one of the many subsections of asexual orientations. Most asexuals can fall in love and want to enter romantic relationships, though whether they have difficulties being in a relationship due to their sexuality is a different issue altogether.
Due to the prevalence of aromantic asexuals in media, this trope focuses on the ones who aren't aromantic. This in itself can lead to tension as most asexuals don't date other asexuals. How to make the relationship work, despite one partner not being asexual, is a common source of drama. Some couples are fine being a Chastity Couple while others do have sex.
Compare to Trans Equals Gay for other LGBT-related misconceptions and Puppy Love for a romantic relationship between people who are usually too young to feel sexual attraction. Related to Chastity Couple, which is about positive depictions of (usually non-asexual) couples that have a sexless relationship.
- It's implied in Sweet Blue Flowers that Akira might be asexual. This leads to complications with her lesbian love interest, as she's unsure if she likes her back, but the manga's ending shows them still together in the future.
- Part of Gender Queer: A Memoir revolves around Maia's asexuality and how it effects eir relationships.
- In Ace, a fanfiction set in the Deep Dish Nine alternate universe of Star Trek: Deep Space Nine, Odo and Ziyal are romantic asexuals.
- The fanfic Ace of Hearts focuses on Keima Katsuragi coming to realise he is heteroromantic, but asexual.
- In RWBY: Scars, Ruby's sister casually note that she's asexual in a discussion. Ruby also has a girlfriend, Penny. For that matter, Penny is a robot (albeit with a human soul) and it's never made clear before she dies whether she experiences sexual attraction either.
- Q from so you were never a saint identifies as panromantic-asexual. He "fancies everyone" but isn't a big fan of sex. And in case people don't understand how that works, he has a "Liking Someone Is Not The Same As The Whole Genitals Thing" Powerpoint prepared to save himself from having to explain.
- Kelsey in City of Angles has been confirmed by Word of God to be somewhere on the asexual spectrum. She has a mostly sexless romantic relationship with her boyfriend, although she is sometimes sexually attracted to him.
- Granny Weatherwax of Discworld is all but explicitly asexual, never having any interest in sex and usually being disgusted when it's brought up (although this may be because it's usually brought up by her shameless best friend who really got around). She remains a virgin all her life, but had one notable romance in her youth, although it was ultimately dropped in favour of her witch career. She briefly reunites with her Old Flame in Lords and Ladies during a period where she experiences glimpses of an Alternate Timeline where she accepted his proposal, and while she doesn't appreciate his attempts to pick up where they left off, she admits that the alternate version of her seems happy enough with him.
- How To Be A Normal Person by T.J. Klune is a Queer Romance novel about a man named Gustavo meeting an asexual stoner named Casey.
- Perfect Rhythm by Jae is about a female pop-star named Leo who goes back to her home town and falls for a nurse named Holly, who is asexual.
- In The Posterchildren, it's revealed at the end of the first book that one of the main characters, Mal Underwood, is gray-asexual heteroromantic.
- April from Stranger And Stranger once dated a boy but dumped him due to her discomfort with sex and hearing about sex.
- Alice in the book Let's Talk About Love is biromantic and asexual, and has a girlfriend at the start of the book. After they break up, she falls in love with a man named Takumi who works at her library
- In the Wayward Children novel Every Heart a Doorway, the protagonist Nancy Whitman is asexual and notes that she feels no sexual desire for anyone. She does note though that she isn't aromantic though and develops feelings for one of her classmates, a transgender boy named Kade Bronson.
- Corin Cadence from Arcane Ascension is asexual and seems to mostly lean toward homoromantic. Overall he appears to be romantically attracted to any human that he can have an engaging and intelligent conversation with.
- Not Pounded In The Butt By Anything And That's Okay, by Chuck Tingle, focuses on a romantic relationship between protagonist Ken and a muscular dinosaur.
- If I Know You is an online fantasy novel about an asexual prince named Roran who is in an Arranged Marriage with a princess.
- Jade Sinclair (codename Generator) from the Whateley Universe. A side effect of being stuck at the physical age of eleven is that she experiences no sexual attraction, which includes being unaffected by Sara's lust aura. While she does have a lot of romantic fantasies they're mostly of the preadolescent, non-sexual "pretty princess" variety.
- In Robin Hood, Sam Troughton once stated that he envisioned his character Much as being asexual, presumably heteroromantic based on his Love Interests.
- Emmerdale: Liv Flaherty came out as asexual, spoke openly about it, with both her family and friends, and they're doing a storyline where she's going to go into a romantic relationship where she explains to the boy she's dating that she's asexual.
- In Sirens (US), Voodoo is asexual, but dates co-worker Brian, ostensibly out of pity and fully expecting that he'll get tired of not having sex and dump her. However, Brian stays completely faithful to her, turning down offers of sex from other women and not even engaging when Voodoo drags him to a strip club. Having realized that Brian wasn't just looking to "fix" her, Voodoo dumps him in hopes that he'll find someone willing to fulfill his sexual needs... only to realize afterwards that she's developed romantic feelings for him.
- Parvati, one of the first companions you meet in The Outer Worlds is asexual and is romantically attracted to women. When discussing her asexuality with the player character, the player character has the option of also identifying as ace.
- Alvin in Backstage Pass, confesses to Sian that he really likes her and thinks she's attractive, but doesn't feel any of the feelings associated with arousal. They decide to explore their relationship further from that point.
- Virginia in Magical Diary is willing to have a relationship with the protagonist, but admits she isn't interested in doing more than kissing and cuddling with anyone and worries that this will eventually cause problems for them as a couple.
- Rohan in When Aster Falls is very clear about being asexual from the start, and the succubus Aster (originally sent to harvest energy from her through sex) is nothing if not relieved. By the end, however, the pair form a romantic connection. Wordof God states that Rohan is asexual homoromantic.
- The Urban Fantasy webcomic Ignition Zero stars a homoromantic ace named Robbie. He falls for another asexual man named Orson. Robbie explains being homoromantic to his roommate in an early page.
- Ace from Kimchi Cuddles is asexual and biromantic.
- The main lead's love interest in Rock and Riot, Carla, is a panromantic asexual.
- Carla Rutten of Dumbing of Age is an asexual homoromantic trans woman.
- In A-gnosis' comics on Greek myth, Athena is asexual and biromantic. She has some early insecurity about her orientation, but Aphrodite — who, as the setting's Love Goddess, definitely knows — reassures her that love can exist without desire as easily as the opposite.
- In Sister Claire, Catharine is a romantic asexual in a relationship with another woman.
- Chanel from the webcomic Rain is an asexual lesbian, and is in a relationship with non-asexual lesbian Maria.
- Shades of A (NSFW) is the story of Anwar, an asexual man who "doesn't want to do more than cuddle", entering a romantic relationship with Chris, a gay man who's active in the kink scene.
- Under the Aegis has Nen, who is only hinted at being biromantic, but Word of God is that is the case.
- Jake from the web serial novel Arrow and Ace is aromantic. Together, he and Sai form the titular aro and ace.
- In the web-novel Fragile, Severin is asexual (although not aromantic, as the story is about him falling in love). We find out in its sequel, Perpetual Change, that it may be the result of being sexually abused by his sadistic aunt as a child. One of the other characters in the story, Helen, turns out to be asexual as well (and aromantic too, according to her).
- In the you could make a life universe, Thomas is hopelessly in love with his best friend Anton but isn't sexually attracted to him. His struggle to reconcile both of these facts makes up the main plot of his series.
- Bojack Horseman: Todd comes out to his high-school sweetheart, Emily, in a diner during the Season Three finale. She accepts his asexuality and they date for a while, but they later end up breaking up because her own needs aren't being met. He also briefly dates an asexual woman, but they have little else in common and break up.