Exactly. We play more than one character side-along all the time, and each character's sheet pertains only to that character and deals with only that character's resources.It struck me to think about a player with two characters - two character sheets. I can readily picture the characters separated in the game world, in circumstances normally expected to forestall them availing themselves of one another's resources. 'These' resources belong to this character, 'those' resources to that one. There seems to me in this case something beyond only resources the player controls. We might add further parameters: the location of those resources, which... character (?!) they are available to? At some point I find it easier to call character sheet a record of the character's resources.
For example, if I'm running both Aloysius and Bjarnni in the same party and Aloysius loans Bjarnni 500 g.p. that loan gets noted on both sheets. (though usually I'll try to avoid having my characters share resources this way; I'd have had Aloysius ask someone else's PC for the loan first)