Why is this chess puzzle alternate line wrong? please need help.

Chess noob here. i want to know, the correct move here is queen D4 instead of queen C3, but i feel it leads to the same outcome of bishop F6 or mate in 2? This is a puzzle on this site rated at like 1200ish IIRC and tested that C3 is incorrect but couldn't find a clue why, so i need some explanation how it is wrong.

I think black must go Bf8 to stop Qg7# but if you put the queen on d4 instead of c3 you can then play Bc3 and threaten mate on h8 which looks crushing.

Thank you, i didn't see bishop f8 for bishop c3. D4 is correct then.

Similar question. I posted this on the puzzle's page, but as no one seems to comment on those I decided to comment here as well. Anyone know why Kg3 or Kg4 would be incorrect? 

In the puzzle on post #4, moving 3...Kg3 or 3...Kg4 allows the Black king to infiltrate into the f-file. Once that is done, the prospects of good pawn promotion is close to nil.

We must not allow the opposing king to get to f1 or g1.