Most stories have a beginning, middle, and end. Even a show about nothing has something zany and inane happen to our characters every episode, while getting some amount of resolution by the end. However, the same isn't necessarily true for a series as a whole. Some series are so homogeneous in plot you could air a season 1 and 5 episode side by side without telling the difference. Others have such intricate plots, you can tell which quarter of which season you're watching just by looking at the subtle nuances of the main couple's relationship.
To quantify this, the Sliding Scale of Season Transition Fluidity (Season Fluidity for short) puts episodic series on one end, and series with self contained seasons on the other. For example, Gilligan's Island is unchanging from season to season. Toward the opposite extreme, seasons in Pokémon: The Series and Blackadder are basically separate shows with an identical or slightly-shifting cast (and some shows don't even have that commonality between seasons — see Skins, below). In the middle, a show like Stargate SG-1 has no distinct seasons, but is threaded together by multiple subplots while staying episodic.
Put another way, you can watch any episode of Gilligan's Island and be equally entertained, without worrying that you've missed important plot points (it's not like they'll ever get off the island or something). While that's also mostly true with Stargate SG-1, seeing more episodes in order lets you see character development over time and several subplots rise and get resolved, letting you get more enjoyment over time. Also falling into the middle part of the scale are series like Game of Thrones or Mad Men that need to be seen with all the seasons in order if one wants to fully "get" them. Moving toward the abrupt end, you can start with the beginning of any particular season of JoJo's Bizarre Adventure, but you will be left scratching your head if you start in the middle of a season.
The far abrupt end would feature shows that do a complete series reboot with each season to the point where they really are completely different shows joined under the same name or following a broader concept. An example of that would be Skins, which starts with a completely new group of characters (save an occasional Ascended Extra or two) and storylines every two seasons, as the old characters graduate from Roundview College and leave Bristol. Other than the setting and the general focus on sex, drugs and parties, each new "generation" (as these two-season sets are known) is completely distinct from the others, and many Skins fans see them as entirely separate works. Lots of fans of the show start with a later generation and then watch the older ones, and are no worse for the wear. Series on this end can sometimes function as an anthology series, but on a season rather than episode level: examples of this include American Horror Story and True Detective.
The popularity of these formats have waxed and waned throughout television history, though with a general trend toward more abrupt forms. Before home video, when shows lived and died on their ability to be discovered via channel-surfing and potential for syndication, fluid series were necessary; you could not expect every viewer to follow the series straight through beginning to end. While series-long arcs were possible in the broadest sense (think Star Trek: The Original Series' "five-year mission"), they could not be too complex; they needed to still be understandable for someone tuning in halfway through season 5. With the rise of home video and especially DVDs, it became more possible for shows to make back money from video sales, making series with longer arcs more possible — though most viewers still discovered television casually, and shows had to remain accessible to them. (Series from this era that required more sustained viewer attention often received lower ratings for it, even if they're remembered fondly now; for instance, The Wire risked cancellation several times, and only started to gain its reputation via DVD sales during its later seasons.) In the age of streaming, though, series that are both less episodic overall and have very distinctive seasons have become more possible, with more mainstream viewers (not just diehard fans buying the DVD box sets) favoring "binge-watching" them in large chunks. In the case of sites like Netflix that release full seasons at once, highly abrupt seasons are the norm rather than the exception — and their popularity has led other networks to do the same even if they release in the traditional episode-by-episode fashion. This is while you'll find dramas from the 1950s-1980s closer to the fluid end, 1990s-2000s ones in the middle, and those from The New '10s and onward further toward the abrupt end (though not always all the way; a purely serialized drama would be closer to the middle because its seasons all follow the same longer story). Comedies have remained more fluid, but even then there is a general trend down the scale; contrast I Love Lucy with something like Community, for instance.
It is worth nothing that not all series fit neatly into these categories, including some of the ones categorized here. Most series have multiple plots going on at the same time, which can have different levels of fluidity. The question comes from which tends to take precedence in differentiating episodes and seasons, which often has to do with where the storytelling places its emphasis: do viewers remember it for its distinctive scenes, episodes or seasons? Buffy the Vampire Slayer has many distinctive episodes, and some broader arcs like character relationships and Buffy coming into her power, but its storytelling is organized around its season-long plot arcs, putting it more toward the abrupt end of the scale. Star Trek: Deep Space Nine has plenty of episode-level stories and smaller arcs, but anchors them in the Dominion War Myth Arc in its later seasons. Yet all of this is subjective, because not every viewer watches for the same reasons. Some shows have been placed in-between categories to demonstrate the categories' (ahem) fluidity. For instance, Glee is known for its individual "themed" episodes and tends to follow the Half-Arc Season, but it has enough dramatic shifts in cast and character dynamics between seasons (especially in later ones) to keep them more distinct.
Note: For simplicity's sake, this scale is excluding (episode-level) Genre Anthology shows, sketch shows, and other works where there is no status quo to either follow or violate, or semi-consistent set of characters/themes. If these works fit on the scale at all, they would mostly fall on the extreme Fluid end.
Sliding Scale of Season Transition Fluidity
|Fluid||Status Quo Is God on the series level, even including Negative Continuity||Most Golden Age and Dark Age Western Animation plus later works that follow those formats (e.g. Animaniacs, Tiny Toon Adventures), most traditional SitComs, Preschool Shows, South Park in its early seasons, Space☆Dandy|
|All stand-alone episodes, no arcs, but with some degree of continuity (e.g. dead characters stay dead)||Star Trek: The Original Series, Star Trek: The Next Generation (early seasons), and most other shows that follow the Adventure Towns or Monster of the Week format; most adult animated comedies including Family Guy, The Simpsons, and later seasons of South Park; most modern Sit Coms.|
|Usually stand-alone, but occasionally has arcs||Doctor Who (classic series), Law & Order and its various spin-offs, Star Trek: Voyager, The Vicar of Dibley and other standard Brit Coms, most Millennium Age Western children's cartoons. Typical abruptness limit for Western Animation and SitComs before The New '10s.|
|Dammed||Series-long Myth Arc or Arcs||Babylon 5, Doctor Who (revival series), Game of Thrones, House of the Dragon, The Lord of the Rings: The Rings of Power, Orphan Black, Star Trek: Deep Space Nine (later seasons), most anime and Noughties Drama Series. "Peak TV" prestige dramas start to show up here.|
|Multiple smaller arcs not directly tied to seasons||Haruhi Suzumiya, Stargate SG-1 (except for seasons 8 & 9), Star Trek: The Next Generation (later seasons), Star Trek: Deep Space Nine (early seasons), Xena: Warrior Princess, most Soap Operas|
|Community, Glee and other serialized comedies; Succession|
|Self-contained season-arcs, with some overarching plots||24, Angel, Damages, Mad Men, Skins (seasons with the same cast), most Teen Dramas and Prime Time Soaps, most Netflix original series|
|Buffy the Vampire Slayer, The Wire|
|Highly-distinct seasons with Arc Welding||Avatar: The Last Airbender and The Legend of Korra, Digimon (first two seasons), Power Rangers, Sailor Moon, Star Trek: Discovery|
|JoJo's Bizarre Adventure, Pokémon: The Series|
|Abrupt||Highly-distinct seasons, self-contained, sometimes to the point of Thematic Series||American Horror Story, Blackadder, Digimon (third season onward), Lexx, Skins (every two seasons), Super Sentai, True Detective|