There's quite some overlap, but generally a consultant is more specialised and has a higher billable rate and works on shorter term projects than a contractor.

e.g. my company currently has a couple of Navision consultants doing integration work for our invoicing system. Once the project is done they'll probably leave. I imagine they bill a lot per hour. Contrast to me (contractor) working on multiple projects, and I've now been there for 1.5 years.