Lotion is runnier in nature and is designed to go through a pump or a tube. It has more liquid oils and distilled water in its formula. Lotion is often better for oily skin and for olivey Mediterranean type skin.
Cream is thicker and so needs to be bottled in a pot or jar as you would need to be able to get your fingers in, to take out a dollop.
Butters are extremely thick and rich (similar to the texture of real butter) they are ideal for dry skin. Due to their very thick nature, they can never be found in a bottle with a small opening or a pump.