Chokes are used to suppress noise, i.e. to prevent noise and other EMI both from entering and going out of some piece of equipment.

What is usually referred to as common mode noise or as differential mode noise are simply two modes in which noise can be coupled conductively (i.e. through wires) into the piece of equipment.

This document explains in more detail the issue.

Essentially common mode (CM) noise is an unwanted signal which couples into both line conductors in the same direction, whereas differential noise is coupled into a single conductor. For simplicity I'm talking about noise coupled into mains line here, where common mode chokes are frequently used, but the same problem arises whenever some wire comes out of an apparatus, for example the leads of a multimeter, an oscilloscope probe or even the USB cable connecting an external HD to the PC.

Common mode chokes usually have two separate windings which are each put in series with each line conductor. These two windings are wound on the same ferromagnetic core in a way that exploits the different path that power line current and CMN currents take in the circuit. Therefore the choke presents very little impedance to the power line current, whereas common mode noise currents see each winding as much higher impedances, and this attenuates the amplitude of the noise.

Another interesting document is this application note about line filters in switching power supplies.

One thing to consider is that you will never achieve 100% elimination of conducted and radiated noise. The regulators know that too and take that into account when the standards are written. So it is necessary to just attenuate the conducted or radiated noise down to an acceptable level.

One way to picture things for selection of noise filter chokes is to consider the choke (or filter bead) impedance as part of a impedance divider. The other part of the impedance becomes either the source impedance of inputs or load impedance of outputs as referenced to the GND system. This can even be dealt with on an intuitive basis so that if, for example a power supply, as an input has a source impedance that is very low then the filter choke probably does not need to be one with an extremely high impedance at the frequencies of interest.

Similarly for an output if the signal terminates into higher impedance load then the high frequency impedance of the filter choke/bead needs to be much higher.

It also seems to be that high current filters are typically lower impedance chokes than the ones selected for low current signal lines.

Last comment I can make is that the proper thing to do in a product design is to think of how you want to architect your EMI suppression and the design support for that into the product using the best layout practices that you can apply. The key thing here is to select proper types of components and have footprints for them available in the design. Then when you build up first boards apply experience to populate the filter bead, inductor and capacitor sites with components with the best guess values. This permits you flexibility to swap out component values at the test lab in case problems are seen in particular parts of the product at certain frequencies.