Check mate vs. stale mate

I keep struggling with stale mate situations, I read so many explanations but I still don’t understand. Here I have an example from a Chess Ultra game vs. a bot. 

I play white. My move was Qf8 because:

- Black king cannot take white bishop because queen would jump on it

- Black king cannot go g7 because queen would diagonally take it

- Black king cannot go h6 because rook would take him out

so black king has nowhere to run, and i can’t understand why this is stale mate? Could anyone explain this to a dummy? Thx!

It's in the name: "Check"mate.  The king has to be in check for it to be checkmate.  Otherwise, it is stalemate.

https://support.chess.com/article/682-what-is-stalemate

what is that piece on h8?

Thx @alramech this looks like a good explanation.

@Chess_player_lol its a bishop, why?

King is not in check, has no moves, and no other piece can move = stalemate.

King is in check and has no moves (and no other piece can deal with the check) = checkmate

For a second I thought there was a white king on h8

It's quite a sad scenario, but stalemates are treated as draws under the laws of chess.

This varies across different board games - stalemate is a win in Xiangqi for example.

Quick quiz – find a significant error in that article.  I used the report-an-error link at the end of that page a few days ago, and it's still not fixed.

Okay, I give up, what is the significant error?

In the second position, the board setup is backwards.  Presuming that black is moving up (it's the only way it could be stalemate), the labels 1-8 on the squares are reversed, and so are the A-H labels.  I found it quite confusing and it definitely needs to be fixed.

In some chess traditions, we end the game when the king is actually captured.  I think the difference between stalemate and checkmate make the most sense when you take it that far. 

A checkmate is when a king is in check, and the king has no available moves to prevent from getting captured.  He will be captured on the next turn no matter what the player does.

A stalemate is when the king is not in check and no piece is able to move.  Remember, a king is forbidden to move into check.  In your example position, the king can happily sit on his square and not be captured the next turn but cannot move to any other square without being captured.   Also, the pawn is blocked as well.  Since black has no legal moves, the game is a draw. 

Personally I'd say the board is set up the right way, but be that's as it may, it's not just confusing it's outright wrong.

Nobody seems to check comments on the instructional pages, but it'll probably be fixed eventually owing to @Rocky64's post on this page. (A few days might still be optimistic though.)

Can't for the life of me see why your first position is checkmate. (If the queen had captured on g8 instead of the pawn it would have been.) The second is stalemate only if it's Black's move.