Back in the days when we could regularly go to garden events, we would see vines crawl across a part of the venue. We sometimes mistake pergola for a trellis and the other way around but they are actually two different elements of hardscapes.
While both involve the use of vines or similar plants, the difference is quite distinct.
A trellis is simply a latticework built so that vines can climb it. It can be a panel attached to a part of the building wall or a free-standing structure with matting or a screen.
The pergola, on the other hand, is a structure built over a narrow path or terrace which is often also used for climbers or vines. The major difference is that the pergola has a column or a post and has a wooden framed roof without sheathing. It can be used to connect one building to another.
So, when you see a roof-like structure that has vines and climber plants on it, that is a pergola and if the plants are on the wall, then, it must be climbing on a trellis.
References:
Robyn Doyon-Aitken, Chip Harley. “What’s the Difference: Trellis, Arbor, and Pergola”. Finehomebuilding. Retrieved August 4, 2020.