A splitter in two scenarios; to couple the signal being received by two separate external antennas (800MHz+1900MHz=Dual Band system), or two split signal from an amplifier evenly among 2 internal antennas (shown below). This is only recommended when both internal antennas are the same distance away from the amplifier.

In this scenario, both internal antennas are the same distance from the amplifier, hence the use of a splitter instead of a tap

A Tap is used as an access point in a multiple indoor antenna system (shown below). The difference between a tap and a splitter is quite simple; one of the two ports is given more signal than the other to compensate for the loss of the additional cable leading to the final antenna. This keeps both antennas balanced, and emitting equal (or similar) amounts of signal.

In this scenario, one antenna is 30 feet further from the amplifier than the first dome antenna, hence the use of a tap

There are also some scenarios in which a tap would be used to provide an antenna with less signal on purpose regardless of its distance from the amplifier; this is most often because of the antenna's placement (in a hall corner, etc.).

An attenuator is very similar to a resistor, in that it decreases gain by a particular amount. Dampening signal is required in some scenarios to keep the amplifier from overheating/overloading, or producing too much signal and oscillating.