Well, kind of, depending on semantics. Most piledrivers are delivered with the opponent's back facing the attacking wrestler. I.E. the Punk/Cena piledriver at MitB 2013 or Jerry Lawler's famous piledriver finisher. A "tombstone piledriver" is another name for the reverse piledriver, where the opponent's body faces the attacking wrestler.

Reverse or tombstone piledrivers are typically super fucking dangerous. Owen Hart botched a sit-out tombstone and compressed and broke Stone Cold Steve Austin's neck in one of the incidents most cited for the WWE ban. They're specifically more dangerous because there's less room to shift your head forwards and take the impact on your shoulders compared to a traditional piledriver (considering there's like, a whole other body in the direction you want to move your head). That said, the only thing that makes a piledriver a "tombstone" is the orientation of the wrestlers' bodies.

That said, Kane and Undertaker do a kneeling tombstone piledriver, which is much much safer than the sit-out version because so much impact goes from the thighs to the shoulders (as you said) and the legs of the wrestler delivering the move act as a stop, preventing head-to-mat contact. Since their kneeling tombstone piledriver is the only tombstone piledriver in WWE since the 2000s, it's easy to lose that little bit of semantics in the mix.