tldr;
DigitalOcean is a "cloud" VPS provider. You get your usual VPS server from them.
AWS is a full blown cloud provider with services that allow you to actually build a complete datacentre (the options are mindblowing).
Heroku allows you to quickly publish web apps by pushing your code up to a git repository (they offer an abstraction layer). Trouble-free POC heaven!
Google App Engine is a service similar in a sense to Heroku (different features, however).