both + noun...both people, both books both of + pronoun....both of them, both of us

Truthfully, there is not a big difference. If you want to get technical: 1. "Both" can be a noun and an adjective 2. "both" by itself is an adjective 3. "both" in "both of" is a noun Examples: 1. I like both paintings. (adjective) 2. I like both of the paintings. (noun) Source: American English (self)