Is the wireless Xbox controller that is sold with the wireless adapter any different from a regular wireless Xbox one controller?

My 5 year old seems to have done something to my left thumbstick. I’ve tried recalibrating it several times and it still has horrendous stick drift.

The controllers seem to look exactly the same and have all the same buttons, but I just don’t know if something is slightly different internally.

I’d way rather just have to spend $40 for a new controller vs $72 to buy the exact thing I need to replace.

I’ve looked online and found a couple answers saying yes but there was connectivity issues, but they weren’t using the official Xbox branded wireless adapter so I can’t really trust that.

Let me know, Thanks In advance.