Leggings are skin tight all the way down the legs and stop at the ankles. Yoga pants are tight to the knees, then flare out below the knees and are looser and longer and go all the way down to the floor over your shoes and usually drag a little.

Yoga pants are made out of a slightly thicker material. They often come with fold-over waist bands and they come in skinny and bootcut/flare cut. Leggings are made out of a slightly thinner material and only come in a skinny cut.

Yoga pants are looser, and I think they look a little less formal, but it depends on how the person is wearing them. leggings are more tightly fitted.