Theoretically, the only difference is in the file size. AIFF is uncompressed, i.e. full size audio file. Most of the lossless files are compressed without loss (hence the name!!), i.e. the redundant data in the file is reduced/stored as single piece of information and so, the file size is smaller. When accessed (played), the redundant data is restored and therefore gives you the same quality audio as AIFF.
The variation in different lossless formats comes about in how and which data they define to be "redundant". But, that is a completely different discussion altogether.