Basically, the two campaigns each show "what would have happened" if its respective faction would win the war.  As such, they're two separate stories.  As for which campaign ending is canonical; the sources we have available say that both Tiberian Dawn and Red Alert 2 follow on the events of this game's Allied campaign.  However, RA2 (and by proxy RA3) don't take place in between RA1 and TD according to former C&C; designer Adam Isgreen, but exist in a separate "universe" altogether, rendering them spin-off games by definition.  Hope that cleared things up.