At the point that we have a contract with someone, by law we represent that person and must protect their fiduciary interests above our own. We must start to interpret for the buyer or the seller what we are seeing and what we know about a property , the area and the community and how that will affect the buyer or the seller and their interests.
Now, while many people refer to someone as a buyers agent, indicating that, that person works with buyers, and a sellers' agent works with sellers, in many companies in MO, that person may really be a designated agent. For example, in my company we have over 3,000 agents. If we were truly buyers agents or sellers agents we would have to share all of our clients information with each other. In a negotiation situation that would be horrible and would not be in our clients best interests. As a result, my company (and many of the larger companies) practice what is called designated agency. As a designated agent, only the agent and the manager/broker know the information on that client. The information is not shared with other agents in the office to protect the client in potential negotiation situations (with that many agents, it is highly likely that another agent in our company may be involved in the other side of the deal when the home is sold).
If an agent is working with a seller and they have a buyer who would be perfect for the home, they may with the permission of both the seller and the buyer, represent both as a dual agent. In that capacity, they cannot provide either side with any information that would give that side an advantage in a negotiation situation. They have to provide the truth and facts, but they must ensure that they do not advocate for either side.
While some agents work only with buyers or only with sellers, most agents work with both. It's hard not to. Many clients have a home to sell at the same time that they are looking for a home to buy and having the same agent represent them in both transactions helps to keep things coordinated and on track far better than having 2 different realtors working on the issues.
A SELLING agent is an agent who represents the seller but brings the buyer to a home. Your agent should explain this all to you in detail, it is not that complicated, but it is a little confusing on first explanation. It took awhile for some of the agents in my licensing class to "get it", too. :)
It depends on the context in which the terms are used. Generally, a seller's agent is the listing agent and represents the seller. A "buyer/seller agent" probably means that person will work for you as a listing agent or as a buyer's agent, depending on your needs. Most broker fall into that category although, more and more, there are agents that will only work for a buyer.