The other type is Dual agency with desiginate agents. This happens when a buyer agent sell the buyer (His client) a property listed by his agency, but not this agent. In that case, the buyer's agent works for the buyer and the listing agent works for the seller.
(It not as simple as this sounds, but it is a common practice in large agencies and is both legal and ethical)
If you wouldlike to call, I will gladly explain in detail without obligation.
Bob Granata 914 668-9514
If this is not happening, this agent is in danger of losing their license and if you have not been provided with what we call Agency Disclosure, find a new agent!