The 4 P's of marketing are: Product, Place, Promotion, Price. Advertising is a type of promotion and an ad agency would only focus on that part of The 4 P's.
A consultant can specialize in any of the 4 P's or all of it.
//what I learned in college. USEFUL HUH?!
Advertising is a type of promotion and an ad agency would only focus on that part of The 4 P's.
A consultant is one person, an agency is more than one.
I'm not being pedantic either, both entities can accomplish the same stuff, albeit at different scales.
On a more technical level, oftentimes consultants can "come on board" and work with a team, helping them revise their project management techniques, marketing strategies, workflow setups, etc. Generally, ad agencies are given a project and then deliver...deliverables.
Again though, both types can do either thing.
tl;dr: circle jerk