REST is a fundamentally different paradigm from SOAP. A good read on REST can be found here: How I explained REST to my wife.
If you don't have time to read it, here's the short version: REST is a bit of a paradigm shift by focusing on "nouns", and restraining the number of "verbs" you can apply to those nouns. The only allowed verbs are "get", "put", "post" and "delete". This differs from SOAP where many different verbs can be applied to many different nouns (i.e. many different functions).
For REST, the four verbs map to the corresponding HTTP requests, while the nouns are identified by URLs. This makes state management much more transparent than in SOAP, where its often unclear what state is on the server and what is on the client.
In practice though most of this falls away, and REST usually just refers to simple HTTP requests that return results in JSON, while SOAP is a more complex API that communicates by passing XML around. Both have their advantages and disadvantages, but I've found that in my experience REST is usually the better choice because you rarely if ever need the full functionality you get from SOAP.
