Qh5+ means the queen went to h5 and the enemy king is now attacked. The plus is the last thing on the move, after the square and after everything else: Nxf7+, exd6+, e8=Q+, and O-O-O+, because castling drops a rook on d1 and that is quite often check straight away.
A check is not a suggestion. Your opponent has to answer it before doing anything else, by moving the king, blocking the line or capturing the checking piece, and when none of those three exists it was never a check at all but checkmate.
Two plus signs, two meanings
++ is where books stop agreeing with each other.
In most modern annotation ++ is a double check: two pieces attacking the king at the same time. It earns its own symbol because it changes what the defender is allowed to try. You cannot block two lines with one piece and you cannot capture two attackers with one move, so the king has to move. Always, without exception.
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g The laws use the same two characters for something else. Appendix C lists ++ alongside # as an abbreviation for checkmate, and plenty of older English books used it that way. So when ++ turns up in print, read the position rather than the symbol: if the game carries on afterwards, it was a double check.
A plus on a move is not ±
A plus attached to a move is check. A plus in an evaluation is somebody’s assessment of the position, and the two live in different places on the page. ± says White is clearly better. +- says White is winning. Neither has anything to do with a king being attacked, and the full list of symbols keeps them apart.
Nothing in the laws makes you say the word “check” out loud, either. It is a kindness at a club and slightly patronising in a tournament, where your opponent is expected to see it. Announcing check is a question of manners; the plus goes on the scoresheet either way.
Double checks are worth chasing rather than reading about, since they are the engine behind most smothered mates and half the sacrifices that look like magic. The double check puzzles are the quickest way to start seeing them a move earlier than your opponent.