So are "aliases" used in other Perl commands besides these sorts of loops? Is that what $a and $b are considered to be in the sort command?

Yes and yes. Some places aliases are used:

• $_ in foreach, map and grep
• $a and $b in a sort block
• $a and $b in List::Util's reduce function and List::MoreUtils's pairwise function
• Each element of @_ for the actual arguments in a subroutine call
• By packages importing symbols
• By an our declaration, which creates a lexically scoped alias
• You can explicitly create an alias via typeglobs

See also "alias" in perlglossary and Item 118 "Access the symbol table with typeglobs" in Effective Perl Programming.