This topic, as P2u said, is almost impossible to talk about, and Marik, tired of the hammer speed thing, is not without consideration also.
The entire point of hammer speed is to note that this is all that counts from the "piano's point of view", and for the pianist, the most anatomically efficient way to do this is the best.
This knowledge as a basic "gold standard of understanding" allows the pianist or would be pianist to eliminate all the inefficient and physically harmful methods and focus on basically playing from the key, pulling the key down, and using small and helpful movements of the hand, wrist, and arm to assist in sound production.
Also, there is a tendency to talk in a rather "either/or" way about this business... either we're using the intrinsic muscles or the extrinsic.
I don't think it works this way. I think we use all of the physical mechanism, some more than others. And a good deal of it is reactive to the intentioned playing.
As a "for instance" there's this discussion about intrinsic vs extrinsic, and I always have wondered about this. Since we know -- as I recall having actually watched dissection videos and read about this -- that the lumbricals teminate at the medial phalanges, pulling the finger down at that point, this leaves the finger tip (distal phanlanges) "unpulled". However, since the lumbricals are the only muscles in the human body that originate not from bone, but from another muscle, namely the flexor digitorum profundis FDP which ends and controls the finger tip, i.e. the distal phalanges, it would seem that using the lubricals would have a contracting effect on the FDP, thus giving some firmness to the finger tip joint, without primarily using the FDP for playing.
I don't know... just a guess on my part, and I've never read anyone discussing this.(doesn't mean someone hasn't)
And even if it doesn't, I believe we use a combination of musculature during piano playing which
cannot be accurately discerned during play.
Unless it is instructive for the pianist to know this information, again rather unknowable IMO, why do we care other than for discussion/curiosity purposes?
As I said, I think we use a very complex combination of the piano playing muscles, and electrical/contractile activity is present in varying degrees, changing from individual muscle to individual muscle, or groups, or pairs, something like a "1000 voice 3 dimensional piano playing bone/muscle/tendon/nerve fugue that Bach and Beethoven together could not have begun to understand, much less 'compose'."
Even to understand how just one cell of muscle tissue works takes pages of detailed bio chemical, electrical, nerve, mechanical, etc., etc., explanation. (which you can all look up if interested).
Perhaps today, a hand surgeon/pianist/scientist could "wire up" a willing competent pianist, and measure the contraction of all the different muscles involved in piano playing, and tell us how much of this or that is used when playing x, y or z.
It is no wonder that people talk about the physical aspects of playing metaphorically or by example, since other than the most basic things, it is impossible to comphrehend and explain in an understandable manner with any degree of accuracy whatsoever, IMO.