Right, it's going to be a detailed answer not only but it covers most games at least to the PS1 era onwards where emulation was starting to be used or more closer eye on ports.
Since you're using the Amiga as an example, we start off with that. Nearly all arcade ports on the home computers were done by people outside of the original development team, they had no contact with them and the only contact was with the publisher. Much of the time, the publisher were at best given an arcade machine to work on and at worst only had access to the machine. The Taito ports at least generally had some extra assets whether it was a flyer or something. A few times, they even used a console reference like with Action Fighter (based on the Master System version) and I think one of the Street Fighter games that you mentioned had its graphics based on the SNES version. So yeah most ports are actually remakes.
Since they are remakes, it depended on the publisher/developer and their angle. Some really wanted to try their best to get as close as it can and others just did it for the money and not out of quality. So it could vary with different publishers and different developers (it happened more on say the Commodore 64 or even the Amstrad CPC, not so much on the Spectrum or the Amiga, at least officially). It depended on the skill of the artist, some were skilled and some were just amateurs coming from school as their first job. Many games were done in a matter of
weeks never mind months so they were pushed for time.
With the artists, they often used graph paper to do a drawing of the sprites and then used software to do the sprites while looking at the graph paper but they might have tile edited directly. This applied to games in that era, both original and arcade conversions.
Saying that there were a few times where technology advanced towards the point where the graphics could be extracted whether tools or capturing. Sort of what tSR does. Richard Aplin the programmer, sprite ripped the graphics from Final Fight. They still got altered because they were still targeting the Atari ST that had a smaller palette, had it been Amiga only it might have been closer. Strider Returns, an original game also
used this technique. It's why Strider Hinjo is a recolor of Strider Hiryu because they sprite ripped from the first game on the Genesis. I'm guessing since Super Street Fighter 2 Turbo was a late game that they sprite ripped the graphics from the arcade or Capcom gave them assets.
Japanese developers tend to be more closer and faithful towards the arcade ports as they had better access and in the case of some, actually having some of the assets or more closer contact to the original developers. At least in terms of the Sharp X68000.
The obvious thing is the system capabilities and that applied to most games of that era no matter which console or computer. The Atari 2600 or the Spectrum obviously can't do ports 1:1 so with those, its whether they resemble the game at all. Arcade technology was advancing faster than console technology all the way to the Dreamcast so even the most powerful console/computer couldn't do an accurate arcade port unless they are either older games (like Donkey Kong) or the machine had close specs with the console/computer. Each console/computer had a weakness compared to the arcade game. The processor with older games using Z80 and then moving to 68000, some systems either ported a 68K game to a Z80 or to 6502 so it would affect the game. If it isn't the processor, its the resolution (C64, NES, Master System, Amstrad CPC, Game Boy/Game Gear). If it isn't the resolution, it's the palette (C64, NES, Mega Drive, Atari ST, Game Boy). If it isn't the palette then the tile size/sprite limit (pretty much all until the Saturn had this problem, even then Galaxy Force wasn't arcade perfect).
It is why some games out of choice know that they couldn't do an arcade perfect graphically port and did it to the capabilities of the console/computer. Like Vigilante on the Master System, doesn't resemble the arcade but the graphics are tailored to the strengths of the console and is a pretty game.
In short:
- System capabilities, skill of the developer, artist working on the game, technology and time.
It is why graphics vary between platforms, even for the same game. Very rarely that you got the same developer working on the game like the PC Engine version of Pac-Land was actually done by not only Namco themselves but the same staff too. Even then it doesn't always mean 1:1 in the case of Genesis Klax and Fire Shark.