Does a health care provider CPR course cover First Aid or is that a separate certification?

As far as current Canadian Red Cross training goes, the CPR for HCP does not cover first aid.

It does cover topics such as shock & deadly bleeding, stroke, angina & heart attack (as well as CPR, AED, choking) but is not considered enough to be a first aid course.

Typically the first aid course covers more. See the related link for a breakdown of the various courses or check your local training provider.