At this point, Trotskyist is basically a term for Marxists who don't like the USSR and the other governments it inspired.

Trotskyism is often seen as a slippery slope to other, crazier ideas. Posadism is an offshoot of Trotskyism. Some Trotskyists believed revolution would be easier under Imperialism than Stalinism, and became neocons. However, these vary from one of Trotsky's greatest personal beliefs: that the deformed workers state is preferable to a bourgois state. Thus, most manifestations of Trotskyism no longer have any attachments to Trotsky as a theorist.

As a historical figure, he's become a rallying point for those who support socialism, but are not comfortable with what they've heard about Stalin and other Marxist regeimes. Supporters of those governments see Trotskyists as ideologically compromised by Imperialist propaganda and justify their extreme hatred of Trots with the historical examples of those who turned against socialism.

Up until the fall of the USSR it was Trotsky = GOOD communism (not like the BAD communism of the USSR) particularly in European nations building up a veneer of political and ideological distancing from the USSR. It was characterized by constant critique of the USSR, China, and basically any AES nation as "not being REAL socialism/communism/whateverism" and sustaining a nominal love of human rights and anti-authoritarianism (free Tibet, free Afghanistan, free Czechoslovakia, free Hungary, etc). In practice it turned a sort of blind eye to all but the most overt forms of military imperialism from the NATO powers, which is why to this day you'll still have Western socialist leaders like Corbyn take the occasional pro-western stance in the name of human rights. But as Fakename_Bill said these distinctions are now irrelevant in the fall of the COMINTERN, the USSR, and the 4th International. Communism today is mostly led by China, Cuba and Vietnam, all whom have detoured significantly from the dogmatic lines drawn by the USSR back in the day. Any newly resurged movement will either borrow from these AES nations, of will have to forge a new path by necessity. It's not 20th century Russia anymore. Perhaps one day there may be a Fifth International to establish how we should build socialism in the future, and we can (and should) invite the ancoms, syndies, communalists, and so on, but we'll need to build it first.