Altho you do see docs that use the two terms with considerable overlap (in particular, giving "access" a fairly wide scope/meaning), I think that "permissions" (possibly permissioning if you insist) is probably what it means.

i.e. that "access" determines that the user is who he purports to be - authentication, passwords, etc. - a high level thing that can be applied to applications (is the username registered for that particular app.), networks, intranets, etc.

the "Permissions" (habilitations) are what you are allowed to do once you're "in" - i.e. you've got passed the "access" stage. These can either be done on a user-by-user basis or more likely by assigning one or more profiles to a user. These would typically give write access to a number of transactions, read-only to some more, block access completely to yet others (typically by dint of simply being omitted). Or indeed, define a user as "admin" etc. as you have hinted. I have only seen "profiles" used for this, but I see no reason for not calling it roles.

I would avoid "user group" because this can be applied to what is essentially a forum (physical or virtual) of the customers of a particular package/application, where they chew the fat about bugs, suggest enhancements and suchlike fun and games.

It's hard to be 100% certain about this kind of thing, cos usage varies from company to company, but that is how I understand it from what you've posted.