There's an "Advantage" entry in the glossary of REG 6.0.0.
Advantage does not count LS unless it specifies it counts LS (there's an EC card that would have used it if it was a thing).
"Play advantage" only cards in in play. "Board advantage" counts cards in play, set-aside, and LoR (which is basically Guardian, since it doesn't count Redeemed Souls either).