What happens when an OTB game ends?

That's something I don't quite understand.

In videos I often see the players shake hands right after a move, and the game ends with a seemingly unclear position.

I didn't hear any player say "draw" or "resign".

So how did the game end?

Did they actually say something but not recorded in the video?

Or just offer your hand, and the opponent understands you mean a draw or resignation?

Usually in a lot of crying, weeping, sreaming, hugging, and slaps on teh butts like baseball.

As a serious response, they either agree to a draw or one player resigns.  If the position is truly unclear, they are agreeing to a draw.  However, a position which may appear unclear to you may be clearly lost from the perspective of a master.

I actually used to say "I resign", haha but now I just offer my hand and say "good game", when I am resigning.

In club level play, most of the resignations I see are made by knocking the king over, or saying something about resigning, and draw offers are made by saying "offers draw".

At higher levels, the actual process of offering draws or resigning is less clear, but for the players, who understand the position, it is clear what is going on.

One of the players throws their king at their opponent.  This signifies teh end of the game.