Combiner vs mixer vs coupler?
These are typical references to RF analog components where the three of these terms are used in the same context. They are often passive devices but can be implemented as active devices (requiring external power) as well. In the passive RF device world they are the following:

Combiner: This RF device combines two or more signals to a single output and is further described as a "Power Combiner". It is typically a passive reciprocal device: it can be used in the other direction as a "Power Splitter".  This can be implemented as a resistive combiner/splitter (for example put three 50 ohm resistors in "delta form" to create a resistive two way power combiner/splitter which will have a 50 ohm match when loaded at all ports, 6 dB loss between each port and no isolation. Often they are implemented with transformers at lower RF frequencies (10MHz to 2GHz), or with 1/4 wave transmission lines at higher frequencies (Wilkinson combiner/splitter) with internal isolation resistor(s) such that they have isolation between the input ports.  

Mixer: This RF device multiplies the time domain signal presented at two ports and provides the product out. It typically will have an RF, IF and LO port corresponding to "Radio Frequency", "Intermediate Frequency" and "Local Oscillator Frequency". It is often used in frequency translation and phase detection applications as well as many other uses. This is often implemented as a passive device with Schottky diodes in a ring with balanced transformers as a "double-balanced mixer" but has many other forms. As a passive device it is reciprocal (any port can be an input or output) but there are often different frequency ranges for each port. 

Coupler: This RF device has an input port, output port, and coupled port. The signal presented to the input port appears at the output port with minimal loss, while some of that signal is "coupled" off and appears at the coupled port.  The 2-way power divider (which is the 2-way power combiner run backwards) is a 3dB coupler and couples off 1/2 the signal power (although that is exactly what it is, we would typically not call it that). More common couplers are -6 dB, -10 dB, and -20 dB. The theoretical loss of a -10 dB coupler from input port to output port would be -0.4 dB, corresponding to the -10 dB signal that got coupled off. Further, the coupled port is isolated from the output port--- a signal presented there, such as a reflection of the coupled signal or otherwise, would be greatly attenuated (~ 30 dB) at the output port but would travel back to the input port. Therefore you can use a coupler in reverse to inject a signal into a system where the signal is fed into the output, the coupled input is fed into the coupled port and the combined signal will come from the input port with the relative coupling ratio. Similar to the power combiner, this can be implemented with transformers for frequencies from 10MHz to 1 GHz or adjacent transmission line structures at higher frequencies (strip-line and micro-strip forms).  There are also 4 port “bidirectional couplers” which have a forward and reversed coupled port. Basically the 3 port devices simply have the reverse coupled port internally terminated, but many of the bidirectional couplers are made as two 3-port couplers back to back for higher isolation performance.