Connections vs Groups

We are offering a Community platform to businesses using CB, and promoting two features, among many others:

1. Make unlimited Connections (friends, prospects, colleagues etc.)
2. Create a Community and send invitations to your Connections or to non-users to join your community.

I am also assuming that:
A user could be your Connection (Friend), but not necessarily be a part of a Community (Group) that you belong to.
A user can host one community of 500 members, but have only 100 Friends.

Please confirm the above. 

Everything you wrote is correct. Connections is CBs friends system. CB GroupJive just provides community groups as many are familiar with on sites like Facebook.