'STAR TREK: THE NEXT GENERATION'
"ENCOUNTER AT FARPOINT"
With our previous entry, Tom called the futuristic hypodermic a sonic screwdriver but he was making a reference to what he thought was a fictional TV show.
Here, however, Commander Riker's sonic driver is probably tech developed by Starfleet from a previous encounter with the Doctor.
Apparently there is an in-joke sighting of the TARDIS in the shuttle bay on board the Enterprise in an episode of 'Star Trek: The Next Generation'. It would be an "As Unseen On TV" adventure in which the Doctor teamed up with Captain Picard's crew, invoking the Khan-Chekov Principle.
Starfleet must have gained access to another sonic screwdriver to build their own model. We know it can't be the Doctor's because he has had the same one for over 500 years. It just keeps changing its design with each new incarnation of the TARDIS interior. (This was confirmed in the 50th anniversary special "The Day Of The Doctor". The Doctor's screwdriver had been running a program to analyze the molecular structure of the wooden door of the prison in which three of his incarnations were being held.)
As you can hear in the clip above, Riker refers to it as a sonic driver. Probably because the term screwdriver is so archaic as a reference to the tool.
So in this case, the reference does add to the validity of 'Doctor Who' sharing the same TV dimension as 'Star Trek: The Next Generation'.