The pull-up variation in which the hands are positioned with the palms facing you is a chin-up.
A chin-up uses a supinated, or underhand, grip: the palms face the exerciser while the body is pulled upward until the chin reaches or passes the bar. The movement is a closed-chain compound exercise involving the elbow and shoulder joints. The latissimus dorsi remains an important contributor, while the biceps brachii generally receives more assistance than in an overhand pull-up.
The main mix-up is between a chin-up and a pull-up. In the usual distinction, a pull-up uses a pronated grip with the palms facing away. Grip width can vary, and some training communities use the word “pull-up” as a broad label for both versions, but “chin-up” is the clearest name for the underhand variation.
A muscle-up is different again: it combines a pulling phase with a transition over the bar and a dip. Neutral-grip pull-ups, performed with palms facing each other, form another variation rather than a chin-up.