Let’s define these visually.
This is an arbor (an outdoor archway):
An arbor built by Chris Ryan
This arbor was built by Chris Ryan for a customer.
This is an arbor with a trellis (latticework to support climbing plants):
Arbor with Trellis by Randy Boyer
Pergola style Roof on Randy’s Arbor
The pictured arbor was built by Project Manager Randy Boyer for his garden. The top of this arbor is very much like pergola…
There are also pergolas which are posts with a simple roof structure:
Pergola built by Duane Overlock
This pergola was built by Foreman Duane Overlock for a customer.
This is the entrance of the customer’s home which has a mock pergola:
Pergola style entrance