The Amiga version has a bit of a confused history.
Wing Commander for the Amiga is technically a PC port, in that the game’s development team worked on the PC version and someone else did the Amiga version. It’s a little different from the later console ports in that this was (supposed to be) done simultaneously. Where the SNES version was a reaction to Wing Commander’s overwhelming success, the Amiga release was planned from the beginning. If you look at the pre-release material for Wing Commander, you’ll see it includes the Amiga version in the ordering information (and the catalogs printed around the PC release say it’s ‘coming soon’).
WC straddles the point in computer game development where this was an ordinary thing. Before 1990, the market was divided between the IBM PC, the Apple ][, the Amiga, the Atari and so forth. Development of an early Ultima game, for instance, would take place on the Apple ][ while other programmers followed close behind on the other systems in an attempt to release all the versions at once. By Ultima VI and Wing Commander, development was being done for the PC version first and the others second. The next year, no one even bothered with anything but the PC.
But wait!, you’re probably saying, the Amiga version actually came out over a year after the PC did! That’s correct, and there’s something of a story there. Although the Amiga version was advertised alongside the PC version, it was significantly delayed. The Amiga wasn’t a popular system in the United States and Origin didn’t do in-house development. Instead, they hired an expert programmer in England (a man named Nick Pelling), where the machine was huge, for the conversion. Unfortunately he developed a nearly fatal brain disease and the project slipped while he recovered.
In terms of the game itself, there were changes made to accommodate the less powerful Amiga 500. Some of the ‘extended memory’ features were removed (I don’t remember the moving hand specifically, but that seems a likely choice) and there was no 256-color mode (it was visually the equivalent of the PC’s EGA version instead of the VGA we’re mostly familiar with). The music likely sounded better at the time (unless you had a special MIDI setup for the PC) because of the Amiga’s nicer sound hardware. There was a second Amiga version developed for (and bundled with) the CD32 a bit later that brought back the 256-color graphics.
The SNES version was actually much later, releasing in 1993 (three years doesn’t seem like a long time today, but it’s enormous in terms of Wing Commander’s overall development history).