DCJ001,
That was too easy. Let me try again. A player, while pushing his stack forward says 80 but, the total amount is actually 100, and it happens TO BE ALL OF HIS CHIPS. Is the player all-in, or are you going to hold him to his verbal bet?
The questions that you're asking are not at all difficult. They should be answered objectively, impartially, and using common sense.
If a player is pushing forward 100 in chips, without saying anything, cuts 80, for example, and pulls the remaining amount back (cut and drop), the bet is not valid until an amount is cut in place and the remaining chips are pulled back.
If someone announces the amount of a bet (equal to or less than the chips that are pushed forward),
before the chips are cut or released, verbal is binding. Whether or not the chips that are pushed forward are all of the player's chips is irrelevant. He should pull the remaining 20 back, and either call or fold to a raise on the same betting street, or check, bet, call a bet, or fold on a future street.
If someone announces the amount of a bet
after releasing the chips that are pushed forward, the bet is the amount pushed forward.
It is very unlikely that the amount stated and the release of the chips will occur simultaneously. If there's a dispute, the dealer should do his/her best to determine which came first.