Although an "Anti-Hero" once referred to one specific kind of character archetype, over time the term has evolved to cover several, many very different but all having one key aspect in common: serving as contrast to traditional hero types such as the Knight in Shining Armor, The Ace, and the Ideal Hero. Ranking them along the Sliding Scale of Idealism vs. Cynicism lends itself well to a sliding scale of antiheroes, although the original definition exists somewhat outside of it.
Character Development may cause an anti-hero to shift up or down this scale. See the Sliding Scale of Antagonist Vileness for characters that would be the Anti-Hero, but they play the antagonist in the work. Compare with the Sliding Scale of Anti-Villains.
The morality of the scale, starting from the Disney Anti-Hero, goes from unambiguously good to evil, but the specific morality of any particular character is usually an issue of diverse opinion.
Classical Anti-Hero: For much of history, the term anti-hero referred to a character type that contrasts the badass, bitter, misanthropic, violent qualities of the modern day antihero. In classical and earlier mythology, the hero tended to be a dashing, confident, stoic, intelligent, highly capable fighter and commander with few, if any, flaws. The classical anti-hero inverts this by being: plagued with self-doubt, mediocre (or worse) in combat, frightened/cowardly and/or not particularly bright. The classical anti-hero's story tends to be about overcoming his own weaknesses and conquering the enemy. Whether or not that happens heavily depends on the story's placement in the Sliding Scale of Idealism vs. Cynicism. In an idealistic story, they are all but guaranteed to find true heroism by the end - in a more cynical setting, it's less likely.
Disney Anti Hero: This is what the term often means in common speech - a character who contrasts with a squeaky clean Knight in Shining Armor—perhaps a Knight in Sour Armor. The term "Disney" is used, because giving it some thought, this character is a hero, with Heroic Spirit, except that they don't have the positive mental attitude that comes with being a straight hero. Very frequent amongst the Mr. Vice Guy. Like the Classical Anti-Hero, a Disney antihero stands a good chance of transforming into a straight hero over the course of the story once they confront their internal conflicts, find someone they want to protect, etc.
Pragmatic Anti-Hero: These are iffier, but no worse than neutral and some stay in the "good" category throughout. This type is willing to Shoot the Dog or otherwise do what they must do. While some of these share the snarkiness associated with a Disney Anti-Hero, they are somewhat darker than the previous version, as their Anti-Hero status is associated with their willingness to do good through "not nice" actions. Essentially a "meaner" version of the Disney Anti-Hero. They may get nicer and turn into straight heroes over the course of the story, but they just as likely may not.
There is some division in this slot as to the acceptability of lethal force. Some will side against it, but others deem it a viable solution. In the latter case, it is generally a matter of last resort, but they will do what they have to do.
Unscrupulous Hero: These are the darkest possible while having fundamentally good intentions. This type of Anti-Hero will recurrently be extremely vicious. In some cases they might simply live in a very Crapsack World setting, and could have been a "Disney Anti-Hero" in a more idyllic setting. This character may have undergone something incredibly traumatic that made them beyond cynical. Their idea of justice towards someone who made their life a living hell may be serving revenge not as a side dish, but as the main course, because they feel that person fully deserves it; at the same time, these enemies will be unsympathetic to begin with, to the point where getting rid of them would still be doing the world a favor. There is some chance that they may see the error in their ways, get rid of the bloodthirst, and change into a straight hero over the course of the story, but don't hold your breath; a more likely scenario is that they'll remain an Anti-Hero and retain many of their flaws, but shift up the scale to a more unambiguously good type.
Note that there is also a separate flavour of this category, which trades the heroic objectives for somewhat nicer methods, or at least more redeeming qualities. Their objectives tend to be neutral to leaning somewhat unsavoury (but never outright evil), balanced by having lines they will not cross, soft spots for their friends and loved ones etc., as well as often being on the good guys' side, even if only by chance or because it turns the greatest profit. In other words, what a Nominal Hero (see below) would be with a sense of honor. (As such, there is possibility of transition between the two.)
Pay Evil unto Evil is a defining trope for this category. See also '90s Anti-Hero, Byronic Hero and Hero with an F in Good. Particularly cynical portrayals of the Lovable Rogue tend to be the latter variety. More heroic Sociopathic Heroes, as well as more merciful Heroic Comedic Sociopaths are also this at best.
Nominal Hero: While these anti-heroes may fight on the side of good, their intentions/motivations are anything but. These people range from amoral characters who happen to be pointed at the villains for one reason or another, to actively malevolent characters, only considered heroes because the villains they fight are much worse. They often fall under the title of the Enemy of my Enemy. These anti-heroes stand practically no chance of becoming straight heroes; if they do, the very credibility of the story is likely to be threatened.
More merciless Sociopathic Heroes and many protagonists from Lord Byron fit on this trope, as well as many worse '90s Anti-Hero characters, but the tendency was hardly limited to that era, either backwards or forwards. If the conflict is Evil vs. Evil or Black-and-Grey Morality, the anti-hero is the lesser of two evils.
'90s Anti-Hero, Noble Demon, darker Sociopathic Heroes, and more merciless Byronic Heroes, recurrently, but do not always, feature this type of character. When on a team, likely to be a Token Evil Teammate. When Played for Laughs, see Heroic Comedic Sociopath.