Espresso is a distinct way of making coffee. It stands on its own. When you order coffee the odds are 99 to 1 that you will get coffee made at standard air pressure. When you order espresso, the odds are in the United States, the coffee is made with water under pressure forcing the water into the grind. This is not always the case around the world.
Instant coffee is exactly like the name says it is.
Boil water, take a spoonful of soluble coffee from a jar or where ever, pour it into the cup with the water, and presto, instant coffee. There are several processes which can be done to make the basic mix, but all are based on brewing up the coffee in a large kettle and dehydrolyzing the brew. After the water is removed a powder is left. It is similar to making salt. The sad part is it is catching on big time.