English can refer to large cultivated areas made to look "idyllic" and natural, formal perennial borders or cottage gardens. English Victorian gardens are extremely formal with heavy use of bedding plants. English cottage gardens are informal plantings of perennials, annuals, fruit trees and flowering shrubs.
French gardens are usually very formal with parterres, clipped hedges, knot gardens, fountains and are very heavy on hardscape and formality.
Mediterranean gardens are characterized by very upright accents of Italian Cypress, pots of citrus and formal gardens with informal plantings lush with lavender and sages. Very popular in California-style gardens, the Mediterranean style involves a large use of water in the garden.
Southwest is a fusion of Mediterranean style with Southwest desert plant material. Usually more formal and geometric than Mediterranean style.
Japanese gardens master the art of form, space and the color green. Balanced gardens made to resemble nature in miniature can include mountain-shaped stones and hill-shaped pines that have been immaculately pruned. These gardens often incorporate water, gravel, tea houses and koi ponds.
Chinese gardens mostly focus on rocks, architecture, trees and, lastly, other plant material. All elements of this design are highly structured.
Persian/Islam gardens are the "gardens of paradise." The word paradise itself is Persian for garden. They are usually walled gardens separated into quadrants with water down the central axis. There is a very heavy use of fruit tree and scented plants. I consider this to be the progenitor of the Mediterranean style.