You were already provided the answer. Obviously using a disc drive that spins a disc at a high RPM is going to wear out said disc drive faster than just using it very briefly to confirm that the disc is in your drive and then playing it from the hard drive.
And I imagine it's safe to assume that the disc drive is causing more heat generation internally than playing from the hard drive would. Particularly earlier model's like I assume your console is where the hard drive is externally mounted on the side of the console.
So since heat build up isn't the friend of electronics, I would imagine playing a game from the disc drive has more of a negative effect on the console in general than playing from the hard drive would. But as you've been told, hard drives also wear out with use.