What is the difference between rectifier/signal diode and zener diode?
I'll try to answer this simply, I'm no expert myself so it's likely some of the comments will correct me little

Although they are both called diodes they have very different uses. 

Rectifier diodes are used mainly for only allowing current/voltage to flow in one direction. As mentioned in the comments above, the specification values for rectifier diodes refer to the maximum current they can pass in the forward direction and the maximum voltage that can be applied in reverse before the diode begins to breakdown.



Here is an example of a rectifier diode in use, in this application it is known as a flyback diode (google for more information). In this configuration, any high voltage spikes cause by switching off the relay (or any inductive load) pass through the rectifier diode back to Vcc, protecting the transistor. As long as the reverse voltage rating of the diode is higher than Vcc it will 'block' Vcc from passing through it. 

Zener diodes work a little differently, they conduct in reverse and can then recover unlike rectifier diodes. The voltage specification of a zener diode is it's breakdown voltage, this is the voltage that the zener will pass.

 

In this circuit they have used a 5.1V zener diode, if you were to use a multimeter across Vout then you would measure 5.1V, all the other voltage is dropped across the other components in the circuit, in this case a 1K resistor. A 1W zener will safely dissipate 1W before burning up. 

In the circuit example above, as it is absorbing 6.9V dropped across the resistor (12-5.1) then this means the circuit current is 7mA (6.9/1000 [I = V/R]) and so the zener will dissipate 35mW (0.007*5.1 [P=I*V]) Zener diodes are used to regulate voltages in certain applications