In the UK if we have a rig with a 2m in/out antenna and a 70cm in/out antenna socket most people search for a duplexer, yet that is completely incorrect.
A Duplexer is a Cavity filter designed to allow transmission on one frequency and Isolate completely the reception on the close by frequency. Thus allowing a repeater to use One Antenna rather than a pair or more. Cavity filters are more complex of a build than diplexers, triplexers or multiplexers
A Diplexer is a different beast altogether what it does is passively split a high frequency from a low frequency for example one antenna, one input from the antenna, then the diplexer spits the frequencies allowing a low band (ie HF) and a second band ie 2m put basically it takes one input and splits it between two different isolated outputs. Diplexing is used to minimise intermodulation (VSWR) for the split bands.
Likewise a Triplexer is similar to a Diplexer except that it can have three outputs let us say (because I use one) 2m out, 70cm out and 23cm out, these are then converted to one cable run.
You can use diplexers and triplexers in two ways, one you can have a colinear antenna at the end of the run, so your antenna is being fed by two / three input/outputs (not necessarily the same radio transmitter or receiver either) OR you can use one at the top of the run feeding three antennas from one cable, however it would be more common then to use a diplexer or triplexer at both masthead and by the radio.
Multiplexers are the same as diplexers and triplexers only they may cater for more bands, one example of where this would be useful is with a four band mobile rig which has one output, but let us say you have the mobile roof space to run four antennas a multiplexer would be the answer.
Likewise all of the above can be used with power splitters when used with the plexer at the top (as different frequencies require different 1/4λ split. To make clear however, you would be using arrayed verticals or beams to want to use a splitter along with this. (Note a power splitter is often referred to as a phasing harness)