Fiber optic connectors can be divided into three groups: simplex, duplex and multiple fiber connectors.

Simplex connector means only one fiber is terminated in the connector. Simplex connectors include FC, ST, SC, LC, MU and SMA.

Duplex connector means two fibers are terminated in the connector. Duplex connectors include SC, LC, MU and MT-RJ. (Note: SC, LC and MU connectors have both simplex and duplex version)

Multiple fiber connector means more than two fibers (for up to 24 fiber) are terminated in the connector. These are usually ribbon fibers with fiber count of 4, 6, 8, 12 and 24. The most popular ribbon fiber connector is MT connector.

Now let's examine each type of connector closely.
FC Connector

FC stands for Fixed Connection and it was developed by Japanese company NEC (Nippon Electric Co.). It has a screw on locking mechanism and is more popular in single mode applications than in multimode applications. FC connectors are popular in test environments and long haul applications. FC was once the most popular connector but now is being replaced by SC and LC connectors. FC connector is available only in simplex version.

Advantages: lowest insertion loss, excellent repeatability

Disadvantage: Bulky, simplex version only, screw-on mechanism is hard to operate in a busy telecom closet.
ST Connector

ST stands for Straight Tip. ST connector has a bayonet twist locking mechanism and was developed by AT&T in the 1980s. ST connectors were predominant in the early 1990s but now they are being replaced by SC and LC connectors. ST connectors are most common for multimode applications. ST connectors are available in simplex version only.

Advantages: ST connector can be easily inserted and removed thanks to its spring-loaded bayonet locking mechanism.

Disadvantages: Its locking mechanism design are both a bless and a curse. You have to make sure the connector is seated in its socket securely and properly. It may be necessary to remove and reconnect your ST connector if you experience high insertion loss. But if you did it correctly, less than 0.3dB connection loss could be easily achieved.
SC Connector

SC stands for Subscriber Connector and was developed by Japanese company NTT. It is a square shaped push/pull type connector with a snap-in locking mechanism. Because of its easy locking mechanism and excellent repeatability, SC connector has become the dominant connector since late 1990s, especially in multimode applications. SC connectors are available in both simplex and duplex version.

Advantages: Easy push/pull snap-in locking mechanism, low cost, excellent repeatability, low insertion loss

Disadvantages: Bulky footprint. Modern high speed fiber optic networks need more compact connectors. LC connector is almost half the size of a SC connector and is becoming more popular, especially in single mode applications.
LC Connector

LC stands for Lucent Connector and it was developed by Lucent. This is a small form factor connector that occupies only half the size of a SC connector. LC connector looks much like a miniature SC connector. It also has the same push/pull snap-in type locking mechanism. LC has become the most favored connector for single mode applications.

Advantages: Easy push/pull snap-in locking mechanism, excellent repeatability, low insertion loss, small form factor
MTRJ Connector

MT-RJ stands for Mechanical Transfer Registered Jack. MT-RJ is available in duplex only. It houses two fibers in half the size of a SC connector. MT-RJ connectors come in pair of male and female type. Male MT-RJ connector has two guiding pins and female type has two guiding holes. Male and Female MT-RJ connectors are mated together by plugging the guiding pins into the holes.