Arbours and Gazebos are basically big arches with seats under them. An arbour is supposed to have an evergreen hedge planted around three sides for shelter, with a climber growing over the top as a living roof.
A gazebo on the other hand is a more open-plan structure made with trellis; it has an open doorway and maybe windows through which to gaze out at the view. Climbers may be planted to cover and climb over the structure. Both can be used as a quiet spot to read, have a glass of wine or just look at the rest of your garden.
Arches are very versatile structures that can introduce height and shape into your garden. They are ideal for covering with climbers and their uses can include an entrance to a different section of your garden or, if several are put together, they can form a tunnel. Arches can be constructed from metal, machined timber, rustic timber or simply posts and trellis.
Pillars and obelisks are the most basic forms of garden structures. Pillars are straightforward poles set in the ground at the back of a border, allowing climbers to be grown up them. If a row of separate poles is joined with swags of rope they are known as colonnades or catenaries. Climbing roses can be trained to grow along the swags to create a spectacular feature.
Obelisks are generally shorter than pillars and are a more decorative upright structure. They are often used nearer the front of a border or in a pot on which to grow the lighter, smaller climbers. A pergola is really just a traditional, formal tunnel with a flat top instead of an arch. A pergola is intended to be situated over a path or a paved area and is often found in its lean-to form against the back of a house.
You can construct a Mediterranean version by using rustic poles over the top on which to grow a vine or, keep it traditional, and grow something like a wisteria, a collection of clematis or other climbers over it. These structures look at their best when heavily covered with climbers, whatever your choice may be.