What is the difference between pooling and caching?

The difference is simple. Pooling is appropriate if you don't care about the internal state of a particular class / type. Pooling is mainly motivated by technical reasons like performance, latency or memory optimizations.
Caching is all about state. You want to retain the state for performance reasons and store (cache) it in objects between calls. So instead loading the state from the database in every request, you could cache the data between requests in valid objects.

Pooled objects are in an undefined state, but the state of cached objects is always well defined.

[See Page 20 (EJB: Introducing Consistency) in Real World Java EE Patterns - Rethinking Best Practices book]