In Monopoly, can you save an 'advance' card to use later?
No. Cards are resolved when drawn (except for Get Out Of Jail, by explicit card text).

CHANCE AND COMMUNITY CHEST
When you land on either of these spaces, take the top card from the deck indicated, follow the instructions and return the card face down to the bottom of the deck. The &quot;Get Out of Jail Free&quot; card is held until used and then returned to the bottom of the deck.

Source : Hasbro - Rules of Monopoly
The wording choice of &quot;advance token to&quot; versus &quot;advance to&quot; is a distinction without a difference: the token in question is the player's playing piece, i.e., the pawn: top hat, shoe, racecar, whatever.
In the case of cards that say to advance your token, you must advance your token to the designated space when the card is drawn.