The actual difference
Compare the job each one does.
Main question
Building permit: Can this construction be approved under the Building Code and applicable law?
Zoning: Is this use, size, height and location allowed on this property?
Typical inputs
Building permit: Plans, specifications, forms and required approvals.
Zoning: Property zoning, proposed use, dimensions, setbacks and site statistics.
Can one replace the other?
Building permit: No. A permit does not waive zoning.
Zoning: No. Zoning compliance does not replace a required building permit.
Common mistake
Building permit: Starting work because the project “looks simple.”
Zoning: Assuming “no building permit” means there are no location or size rules.
Treat them as two separate checks. First define the work and the property constraints, then confirm which approvals the project needs.
Official sources
Ontario — Building permits
Toronto — Zoning Applicable Law Certificate