Bossa Nova is really a fusion of samba (bass line = boom, ba doom) plus a clave beat on top and steady straight 8s on a hihat, rhythm guitar or shaker. The clave is often on the snare sidestick and can be 3/2 or 2/3 (and often a mess of the 2!)
The jazzier versions of Bossa Nova are really a stage further away from Brazilian music, to the extent that a few Brazilian musicians I know call the Getz/Gilberto collaboration purely North American music. For more "authentic" Brazilian bossa, have a listen to earlier stuff by Gilberto, Jobim of course and Baden Powell.
Once you start getting creative in a more jazz context, as in the Joe Henderson example, it just becomes a sort of vague "latin jazz" genre which can be a fusion of many stylistic elements, either pre existing or invented.