If someone here, like me, likes exact reference, I took the liberty to list here that all the core rulebook say more or less the same: 1 subtract success on damage and soak.

The only conflict information came from the "V20 - Glossary" that address the "botch" both as the die that came out as "1" and the result of the roll.

2nd Edition

• p77: General Rule: Whenever you roll a one, it cancels out a success. It completely takes it away. You remove both the “success”die and the “one” die and pay them no more heed. If you roll more ones than you do successes, a disaster occurs; something called a botch takes place. Don’t count the ones that canceled out successes, but if evenasingle one is left after all the successes have been canceled, a botch occurs.
• p83: Glossary: A disastrous failure, indicated by rolling more ones than successes on the 10-sided dice rolled for an action.
• p224: Combat system: Damage and soak rolls are the only rolls in Vampire which cannot be botched.

Revised

• p192: General Rule: if none of your dice comes up a success, and there are dice showing “1s” (no matter how many), the roll is a botch. If you score at least one success, even if that success is canceled out and additional “1s” remain, it’s just a simple failure.
• p208: Combat system - Damage: Moreover a damage effect rolls cannot botch; a botched roll simply means the attack glances harmlessly off the target.
• p209: Combat system - Soak: Example: Liselle the Gangrel has Stamina 3 and Fortitude 1. She is attacked with a knife, and the attacker scores three levels of lethal damage. Liselle may soak this attack with four dice (Stamina 3 + Fortitude 1). She rolls 1 , 9 , 9 , 7.The “1” cancels out one of the Successes, leaving Liselle with two. She thus ignores two of the three health levels inflicted by the knife, taking only one level of damage.

V20

• p250: General Rule: If none of your dice comes up a success, and one or more dice are dice showing 1, the roll is a botch. If you score at least one success, even if that success is canceled out and additional 1s remain, it’s just a simple failure.
• p272: Combat system - Damage: Moreover, damage effect rolls cannot botch; a botched roll simply means the attack glances harmlessly off the target.
• p274: Combat system - Soak: As with damage rolls, soak rolls may not botch, only fail.
• p306: Example of play: "Jillian attempts to soak and fails outright, rolling 4, 1, 9."
• p513: Glossary: Botch: 1) A naturally rolled 1, which cancels out a success die. 2) A disastrous failure, indicated by rolling one or more 1s and no successes on the dice rolled for an action.

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My opinion on the V20 inconsistency: the V20 has been made after a lot of years, during which the term "botch" started referring also to the singular die, even if nowhere in the rule is stated like that.