Hello,

the differences are explained on the site:

/rest/variant
This call returns all information about a variant in the ExAC database.

and

/rest/variant/variant
This call returns information about the variant itself including the gene that it is in, the frequency of it in the database, and what transcripts it could be found in.

I find it quite clear. What don't you understand here?

Which of the two forms is the one I should use to obtain the minor allele frequency for a variant?

You've started another thread about this. I'v answered you there.

fin swimmer