There are several different types of listing contracts, but very few of them are used. The "Exclusive Right to Sell" is the most common, but there is the "open listing," the "exclusive agency listing," and the "one-time show."
The "open listing" is mostly used by people trying to sell their home by owner who are also willing to work with real estate agents. Basically, it gives a real estate agent the right to bring buyers around to view your home. If their client buys your home, the agent earns a commission. There is nothing exclusive about an open listing and a home seller can give out such listings to every agent who comes around.
For that reason, no agent is going to market your home or put it in the Multiple Listing Service. If your home fits the criteria for one of their clients, and it is convenient, they may be willing to show it to their client. That is all an "open listing" is good for.