Gluteus maximus
The gluteus maximus is the biggest of the three and the one you probably think of the most when you hear glutes. It is the most visible of the three.
The gluteus medius lies right under the gluteus maximus and functions to abduct (or more away from your body) and externally rotate your hip.
It is the smallest of the three and lies underneath the gluteus medius.
The Hip Thrust
The hip thrust is a simple exercise that maximally trains hip extension.
The squat is the king of the lower body exercises and is a great way to build a strong booty.