ST Connector: The ST Fiber Optical Connector greentelftth.com (or Straight Tip) was the first popular connector type to be used as a standard for many organizations in their fiber network applications. Often called the "round connector", it has a spring loaded twist bayonet mount with a 2.5mm round ferrule and a round body. The ST connector is fast being replaced with the smaller, denser SFF connectors.
SC Connector: The SC connector is a push-in/pull-out type connector that also has a 2.5 mm ferrule. It is very popular for its excellent performance record. It took a while to surpass the ST because of price and the fact that users were comfortable with the ST. Now, it's much more competitive with pricing and it is very easy to install, only requiring a push in and pull out connection. This is very helpful in tight spaces. Simplex and duplex SC connectors are available.
FDDI/ ESCON Connectors: You may see FDDI and ESCON(IBM) duplex fiber connectors in older installations. These connectors will mate to their own networks and usually will be seen at the wall outlet locations. These connectors use a squeeze tab coupling mechanism. The closet side of the fiber will usually have a standard ST or SC connector. The FDDI/ESCON connectors can be mated to SC or ST connectors since they both have a 2.5mm ferrule. An adapter would be required in this case. The FDDI stands for Fiber Distributed Data Interface.
LC Connector: It is a single form factor connector that has a 1.25mm ferrule. And it is a smaller square connector, similar to the SC. LC connectors are often held together with a duplex plastic retainer. They are also very common in single mode fiber applications.
MTRJ Connector: MTRJ stands for Mechanical Transfer Registered Jack. MTRJ is very similar to an RJ type modular plug. The connector is always found in duplex form. The body assembly of the connector is usually made from plastic and clips and locks into place. There are small pins present that guide the fiber for correct alignment. MTRJ's also are available in male or female orientation. They are only used for multi-mode applications. They can also be difficult to test because many testers on the market do not accept a direct connection. You usually need to rig up a patch cord adapter kit to make testing possible.
FC Connector: The FC connector you may find in older single mode installations. It was a popular choice that has been replaced by mostly ST or SC type connectors. It also has a 2.5mm ferrule. They have a screw on retaining mechanism but you need to be sure the key and slot on the connector are aligned correctly. FC connectors can also be mated to ST & SC's through the use of an adapter.
Well, the above connectors are just some most commonly used ones, and there are still more types of connectors available in the market.