Thank you, Packard.They are both used. Though film is pretty much gone from TV shows and partially gone from movie production, many of the terms originally used for film are still used. So "filming" is still fine, even when no film is involved.
A few obsolete references that are still current terminology:
In the can: means the film has been shot and is complete (and in the film can)
Cut: an abrupt change in point of view, once made by actually cutting the film
film clip: A short section of a film shown for advertising. It was literally a piece of film that was clipped from the reel.