Terminology

Session Cache

When a client/server connect they establish a session ID which it will try to use later. This session id includes what ciphers they agreed upon, etc.

A client offers to reuse a session ID. If the server recognizes it then they will skip the whole cipher/etc determination phase, which results in smaller overhead. This is called a cache hit. (the session id cache is where these session ids are.)

A session id cache miss means that the client either doesn't have a session id it can use, or the server doesn't recognize it. Thus they negotiate ciphers all over again.

Stunnel from 3.8p1 and later support client session id reuse. Previous versions didn't. All versions support server session id reuse.