definatly a common goldfish. as stated already, comets have longer fins and seem to be a little more sleaker and streamlined, whereas commons are short finned and full bodied.
if she's dead set on another tank-mate, sugest a dojo loach or two. its added bio-load, but they will eat the food that goldfish are so wonderful at spitting out and making a mess with before some of it can foul the water.
bring up short info on an oversized filter, weekly WC's. take 2 minutes to just point her in the right direction, and we may eventually have another fish keeper if she's showing interest in caring for the fish properly