The fastest distinction: pergolas create filtered shade and keep the sky open; pavilions create a solid-roof outdoor room; Belvederes and cabanas sit between them with a more open architectural roof form.
Choose a pergola when the patio needs definition, partial shade, and a lighter visual footprint. Choose a pavilion when the goal is outdoor dining, grilling, or gathering in more weather. Ask about a Belvedere / Cabana when you want a distinctive open structure with more roof presence than a pergola.
The free design step helps compare both options in the actual yard before you commit to a direction.