MusicBrainz Picard can look up discs based on the ToC and disc ID. Other software can implement the algorithm used by MusicBrainz if they wish: https://musicbrainz.org/doc/Disc_ID_Calculation
They do also store FreeDB disc IDs, for example: https://musicbrainz.org/cdtoc/lwHl8fGzJyLXQR33ug60E8jhf4k-
MusicBrainz has its own format of disc ID (checksum of an entire audio disc), plus per-track fingerprints.
Artist credits can be tracked -- there are extremely fine-grained relationship models -- but most entries don't have the associated metadata because it's a hassle to input.
Disc ID's weren't perfect, you can make a pretty easy mapping between the two if you want. But software still in maintenance really should switch to musicbrainz (and probably should have switched long ago).
For my own system I used a music fingerprint written by Giancarlo Pascutto (I hope I spelled that right, it's ages ago), which used a really nice algorithm that did not see a single collision in a very large number of tracks.
Also, ISTM that it should be quite feasible for musicbrainz to track artists and "acts", in a pinch by cross-referencing wikidata.org which acts as a sort of shared focus for the whole Linked-Open-Data metaverse.