Pergola, Gazebo or Canopy
A pergola is a frame with an open or slatted roof; a louvered pergola adds slats that close. A gazebo is a freestanding structure with a solid or panelled roof, built to stay up. A canopy is fabric on a light frame, put up seasonally. The difference is the roof, not the shape.
The distinction that matters
All three cover a patio, and the words are used loosely enough in retail that the labels are almost useless. The question worth asking is what the roof does. Does it move? Does it stop rain? Does it stay up in winter?
Pergola
Traditionally a frame with an open or slatted top - shade and structure, no shelter. A louvered pergola is the modern version: the slats turn and close, so the same frame gives open sky, filtered light or a sealed roof. It stays up permanently.
Gazebo
A freestanding structure with a roof that does not move. The roof material decides the character: solid panels give shade and shelter, polycarbonate gives shelter while passing daylight through. Nothing to adjust, nothing to maintain seasonally.
Canopy
Fabric over a light frame. Cheap, quick, and seasonal - it comes down for winter, and it is the one that fails in wind. Useful for an event; not a structure.
Choosing between the first two
If the patio needs deep shade some days and open sky on others, the louvered roof is the only one of the three that does both. If it needs to be bright underneath whatever the weather, polycarbonate panels do that and a closed louvre roof cannot. What each covers is computed in sizing.
Questions
What is the difference between a pergola and a gazebo?
The roof. A pergola's is open or, on a louvered model, movable. A gazebo's is fixed and covers permanently.
Is a louvered pergola a gazebo?
No. It closes to a roof but the slats still move, which is the whole point of it.
Do canopies last?
They are seasonal by design - fabric on a light frame, taken down for winter.
Which gives more shade?
A closed louvered roof. Polycarbonate panels pass daylight through by design.