In my experience, the manufacturer's drive model used inside may indeed be the same. But then there is the mount, and that is why I suggested you look at the shape of the assembled module on ifixit.
I have found that these drives may be partially enclosed by lightweight aluminum carriers. These may be attached by glue or double-stick foam tape or other diabolical attachment methods that are not simple to remove. In removing these in the past, all I ended up with after a lot of work was a pile of bent aluminum mountings and a bent and unusable drive. It was an exercise in futility.
Because of this potential difficulty, I do not recommend re-purposing the drive from one model into another.
But sites like ifixit and many others will sell you a used drive, with a modest warranty, with exactly the mounting frame you need, for not a lot of money. That is the approach I would recommend.