In HS football, the rules permit the receiving team (usually designated R, not B) to choose where they will take the ball: either the spot of first touching by the kicking team, or the result of the play.
The answers will be different in your two situations. In (1), R will take the ball at the spot of first touching, as you say. In (2) it's more advantageous for them to take the result of the play, which is a touchback. First touching is defined in rule 2-12.
Your intuitions are correct, and now you know why!
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Cheers,
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