Contractors often work onsite for set lengths of contract (3,6,12 months) on one or more projects.

Consultants often work on a single project they bid on in their own time.

It means the same. You can even throw in "freelance" there as well. All terms just means an external person doing work for a company in some form.

Typically you'd associate the "freelancer" with the scruffy php dev who does localpetshop.com sites from home, and the "consultant / contractor" as a temporary, full-time team member in one or more enterprise-scale projects on-site at a large customer.

In reality though, it's all the same.