The CSE is a full-text search engine. You can selectively enable full-text indexing for document body content as well as selected string properties. In CM jargon, you will sometimes see the notion of a text index referred to as content-based retrieval (CBR). That's just another name for the same thing. The internals of the CSE are Verity's K2 engine, but Verity was acquired by Autonomy a few years ago, so you will see it mentioned all three ways—Verity, K2, and Autonomy—in documentation.
The CSE is not a J2EE application, and it runs separately from the CE. In production environments, it is run on separate servers from the CE so that loads can be better managed. In our lightly-loaded all-in-one environment, we'll be installing it on the same Linux server that holds our CE installation. When you look at the CSE topics in the PPG, you will find quite an assortment of different logical server types that make up a CSE environment. You will certainly want to consider...