Licensing covers a whole spectrum of things and since CBS and Paramount were once the same company the whole thing is "fuzzy" since when they separated things were split.
No things are not fuzzy. CBS bought the Star Trek rights that Paramount had several years ago and they got split up. CBS owns the Star Trek brand and all of the IP from the original server all the up to and includes Star Trek Nemesis. Paramount retains the film library (and to make more movies) and the video distributions rights on behalf of CBS.