This traditional mediterranean style pergola is usually made from wood and built against the house to provide a transitory area from the inside to the outside. during the Renaissance period in particular it gave ladies of a certain breeding the opportunity to take the air without damaging their fair complexion.
2) 'Stand-alone' Pergola
Again, traditionally made from wood, features uprights but no solid roof. These can be positioned attractively in the garden and allows some protection from the harsh rays of the sun, particularly if planted up with shading climbers.
Both types of pergola are, in effect, frames for vines and climbers that surround the occupants with foliage, flowers and aromas, offer a measure of protection and, nowadays, afford some privacy in urban areas.
A wooden stand-alone garden structure, usually with sides and a solid roof, frequently situated to maximise available views of the garden itself or the landscape beyond. They are often hexagonal or octagonal in design and may have lattice-work sides and built-in seating, giving them a sturdy, enclosed feel. They are structures in their own right and are rarely vehicles for plants.
Same as above but a modern description on the theme - usually square or rectangular and with glazed windows. Can be plumbed in and have access to electricity for further outdoor usage.
5) Arbour (USA - Arbor)
A short 'walk-through' stand-alone arched structure, usually made from wood, that connects one part of the garden to another (say, the vegetable garden to a formal lawn area). these are often used as a frame for climbers, particularly roses
6) Victorian arbour
A traditional solid wooden garden 'love seat' (popular in Victorian times) - usually with incorporated bench, high back and covered arch for roof. When planted with climbers (roses) the excitement of a clandestine meeting in a garden appealed to the Victorian sense of romance!
A variation on the above - placed in a shady enclosure or recess in the garden, these stand-alone structures, usually made from wood, and with latticed sides and backs, were used for secluded contemplation of the garden and when planted up with climbers - enhanced the additional sensory appeal.
Still on the same theme as above - an alcove is a shady recess, retreat or niche in a garden wall that uses either the wall itself or foliage as a roof for protection from the elements. Some alcoves have a small wooden arch built as a roof if the wall is not high enough or there is no nearby vegetation. C17
A building or garden room having a circular plan especially incorporating a domed roof. C17 - from Italian 'rotonda' and before from Latin 'Rota' meaning a wheel. Mainly built from stone with wooden framed roof.
Popular with the Victorians - built of stone or brick incorporated a glass roof with wooden frame and, sometimes, glazed sides. Traditionally used for growing oranges in a cool climate. Great example of one at Kew Gardens, London.
There are many descriptions of the word pavilion ranging from a large ornate tent with a peaked top used for shelter by kings, princes and generals of armies during the middle ages, a changing room for british cricket players to a temporary structure that is usually ornate and open sided for housing exhibitions. They can also describe the structures, like bandstands, that appeared in English parks during the C19 to the grand Brighton Royal Pavilion on the south coast of the UK built for King George 1V between 1787 and 1823 for his renowned Regency parties, balls and general entertaining.
However, in this context, the term pavilion would mean a summerhouse or other such decorative garden structure that would be a step above any of the terms described so far. You would have to have a great deal of money and space to commission one!