and since some one hit my "attachment ON button"
Gap - basically two sizes, 1/4" and 3/8" there are very few Mfg that take a narrow gap foot.
Distance between bar and needle (or front edge of gap to needle hole) .425", .475" .5" .52" and .62" some feet have an "open toe" so they can accommodate more variation in needle position, but it's still got to be close.
Needle position - Centered in gap, or offset to right or left, and some have a slight offset, some a significant offset. And some Mfg had offset on older machines, and then went to centered on later machines.
There was a time before the top clamp that machines had slip on feet - but the "specs" are the same and with most, you can put the top clamp adaptor on them and use that style feet.