Comebacks are funny. Most of the time, everyone has to be aware of the thing or person that has left and is returning. After all, the Empire cannot strike back if you are unaware of what it was doing before.
This may seem obvious, but it's important to note because once in a while, in big sci-fi narratives, the opposite happens: a comeback is a big deal, but knowledge of anything pre-comeback is optional, or perhaps, irrelevant. 40 summers after Kirk screamed Khaaaaan!!! the true brilliance of this film is how it enticed everyone to remember Khan in the first place.
Khan was a one-off villain in Star Trek: The Original Series, which aired only once in 1967s Space Seed, due to an outstanding performance from Ricardo Montalban. However, his role in the Disney series in the 1970s and 1980s is not established, and so is Mudd's influence in three more episodes: two in Discovery season 1 (2018) and one as Mudd's-centric Short Treks (2019).
The thought of comparing Harry Mudd to Khan is a bit sceptical, perhaps, since Carmels Mudd isn't necessarily more hardcore than Khan. In 1982, VHS tapes of The Original Series were pretty common, meaning, if you remembered Khan, you simply missed it. In 1982, it's possible that all types of Star Trek fans simply hadn't seen Space Seed, or they might have remembered Khan hazily.
Producer Harve Bennett intuited that Khan had made a significant impact on viewers despite only having one episode. Meyer, who had never really watched The Original Series before tackling the film, agreed that Khan was the perfect type of classic character to bring back for the film. It's a bit of a magic trick. Khans story in The Wrath doesn't require the audience to understand jack-shit about Space Seed.
The Wrath of Khan is a sequel to Space Seed with several distinct continuity points. This sort of situation can easily be fixed by head-canon that suggests Chekov was simply working on the lower decks that year and knew about Khan anyway. But this tiny hand wave is actually the tip of the iceberg when it comes to how much punishment The Wrath lets fans for not seeing Space Seed.
Captain Terrell (Paul Winfield) tells Kirk that Khan is liable for the death of his wife. I understand, but why does Kirk know this? The rest of the audience do not know or care about this deceased, off-screen wife.
When Chekov and Terrell discover Khan accidentally on Ceti Alpha V, you know everything you need to know about his background. I mean to avenge myself upon you, Admiral. Thats the Khan of this film, and thats all we really need to know about him. However, Meyer's actions aren't as effective as the original episode.
The Wrath of Khan canon isnt a film about the difference between the Space Seed and the Wrath of the Khan. From the Chekov thing to Khans super-young minions, to the incredible mistake the Reliant makes by confusing two planets, none of the wonky continuity hurts The Wrath. It's the opposite!
The Wrath of Khan was a dark-and-gritty Star Trek reboot that refused to gloss over certain canon details, but nonetheless allowed Khan's literal wrath to exist as a self-contained narrative within the film. We know who Khan is, because he is the guy who brought the Wrath to Holmes, even though he was never there.
The Wrath of Khan is the finest example of a film sequel that infuriates an audience with this kind of emotional retcon, but The Wrath of Khan's legacy is probably most evident in the MCU's ascension of Thanos.
Palpatine's ascension in the classic Star Wars trilogy is similar; he's an offscreen character in 1977 and appears as a random hologram in Return of the Jedi; then, in Return of the Jedi, you're meant to think you've known about Palps all the time, even if you hadn't heard him before the Prequels, which seemed to be influenced by The Wrath of Khan's handling of the villain.
The fact that on its own, The Wrath of Khan is a shocking achievement, as older Star Trek fans often recommend that newcomers begin with The Wrath of Khan. Khan was founded in 1982, thus allowing the whole last frontier to begin over.