Permissions are defined by the corresponding attribute bits of files set by various level of relationship (owner, group, other) or using more sophisticates methods. These bits prescribe what user can do with the file: read, write, open etc.
User rights are defined by his/her participation in various groups, so he/she inherites rights for starting various programs, edit some files, configurations etc.
My advice, for questions like that, get "Learn Linux for a Beginner" DVDs by Unix Academy
Hope it helps