here in New York State they are the same thing...

Alters are parts of a persons personality /self that has been split off from the rest and takes on their own distinct patterns of ways to be, jobs, purposes, and reasons for being.

some have more co consciousness (ways they interact, share, communicate) then others., some are so in my therapists terms categorical that they have little to no co consciousness with each other and the one they reside inside of.

there is actually two dissociative disorders now where a person can have alters / parts / or in your words distinct selves.

DID which is where a person with the disorder with alters, has time loss (amnesia symptoms)

OSDD (Other Specified Dissociative Disorder) where a person has alters (alternate selves) but does not seem to have amnesia /time loss symptoms.

that said other locations, cultures, religions, .....may have a different way of explaining what alters are to those with DID.