What's the name of this variant of Speed?

I was playing card games with my Sister-in-Law and proposed we play Speed. The version I play is where both people have a deck of 15 and a hand of five, there are two stacks of five on either side of the center, and the center has two cards that we pile cards from our hand onto. We place a card either +1 or -1. She was surprised by this.

She then taught me her version (she's Mexican American and grew up in CA):

The deck is split between two people. Each person lays five cards in front of them face up. Then, players play cards face up on top of pairs and three-of-a-kinds. The first person to empty their deck wins.