Contractor is a temporary resource brought in from outside of organisation. Contractors' job is done when they finish delivering products or services specified in their contract.
Consultant is a specific kind of contractor. Their primary job is not just scaling up the existing team, but delivery of knowledge transfer. Consultants invest time into learning a specific topic or coming up with a new way of doing things, then they come to an organisation and transfer that knowledge to the locals, so that the team can carry on doing the job without need for the consultant to stay with the organisation.
There's a much more important (though somewhat cynical) distinction between the two though. A contractor is a guy working for your company on the equivalent of a 1099, who behaves much like an employee. A consultant is an outside entity who comes in to do a specific piece of work, and tends to be treated as something of a specialist who you should listen to. Given that the actual work being done is usually indistinguishable, guess which one you should call yourself if you want to make more money?
There's a 3rd term for this same position, "Freelancer", that you can use if you want to make significantly less than either of the above.
Contractor is a temporary resource brought in from outside of organisation. Contractors' job is done when they finish delivering products or services specified in their contract.
Consultant is a specific kind of contractor. Their primary job is not just scaling up the existing team, but delivery of knowledge transfer. Consultants invest time into learning a specific topic or coming up with a new way of doing things, then they come to an organisation and transfer that knowledge to the locals, so that the team can carry on doing the job without need for the consultant to stay with the organisation.