A cloud application is a regular NSApplication with a few additions made by Objective-Cloud.
An invocation based application is a cloud application which mainly implements Objective-C methods which are then (remotely) invoked by clients. The other kind of application is a request based application. You can have a cloud application which is acting on requests and invocations at the same time: Invocations and requests can be mixed.
A request based application is a cloud application which receives (raw) HTTP requests and creates (raw) HTTP responses. You can have a cloud application which is acting on requests and invocations at the same time: Invocations and requests can be mixed.
Objective-Cloud Connect is where you signup, login and manage your cloud application.