Im not completely sure on AIFF but what Ive heard over the years:
AIFF, the original apple audio file (?)
SD2, an AIFF with timestamping, developed for interop between PT and media composer. mac only.
Wav, the microsoft file
BWF, a wav with a monstrous, agreed, standardised metadata chunk, which is malleable, developed for archiving and longevity, as already mentioned - recommended as a standard, works on mac and pc.
MXF is the Media Exchange Format wrapper, and is in a "non-divergence" metadata agreement with the Advanced Authoring format, the AAF (more open version of OMF). Its Avids native video media wrapper, and sometimes audio comes across with an MXF wrapper as well.
Many broadcasters are going to full MXF output, wrapping it around production assets with video as mpeg longop and audio as dolby E streams being fed into playout servers.
Key thing - if you are in film, you want BWF, untampered, all the way from production through to you. If video change it to AIFF you may lose critical metadata from the BEXT chunk and iXML chunk.