All three are “anhydrous” meaning they don’t contain any water. This distinguishes them from creams and lotions.
Body oils contain only oils and are light in consistency.
Body butters contain a mixture of butters, waxes, and oils making the consistency thick but easy to spread.
Body balms contain high concentrations of butters and waxes making the consistency dense and optimal to use on dry patches of skin—such as lips, elbows, knees, heels, and cuticles.