De-coupling capacitor and Bulk capacitor
There is, in a sense, no qualitative difference. The difference is one of scale, both of current and of time. 

A bulk capacitor is used to prevent the output of a supply from dropping too far during the periods when current is not available. For line-powered linear supplies, this would occur during the periods (say, 10s of msec) that the line voltage is near zero. It also applies to the circuit as a whole. That is, an electronics assembly containing multiple circuit cards might have a single set of bulk capacitors in the power supply.

Decoupling capacitors, on the other hand, are used locally (such as 1 per logic chip in some systems) and are intended to supply current for much briefer periods (typically 10s of nsec for TTL systems) and much smaller currents. As a result, decoupling caps are typically much smaller than bulk caps. 

This is not entirely a hard and fast rule - for some high-speed analog parts a mix of different decoupling values is recommended, with the smallest values providing the shortest compensation times, and larger caps being used as well. High-speed A/D converters often used to recommend a 0.1uF / 10 uF combination. Many logic boards have a mix of values scattered around. CPUs, in particular, are often surrounded by largish (10 - 100 uF) electrolytics, with a whole bunch of small SMD ceramic caps right under the chip.

As for demonstration circuits, only bulk caps make easy demo's. Take a transformer output of, let's say, 6 VAC, and run it through a bridge rectifier. Load the output of the bridge with a power resistor (like, 10 ohms) and look at the voltage across the resistor - it will drop to zero 120 times per second (100 if your line frequency is 50 Hz). Now place a bulk cap of 10,000 uF on the bridge output, and the output will be much smoother, with 120 Hz dips - it will look sort of like a sawtooth - but in general the voltage will be much smoother.

Decoupling is harder. Try setting up an op-amp amplifier on a solderless breadboard using a high-speed op amp and long wires running from the breadboard to the power supply. There's a good chance the output will oscillate with no input. If you put 0.1 uF ceramic caps from the supplies to ground, and do it right at the op amp supply pins, this will often clear up the problem. Or not - solderless breadboards aren't good for high-speed work even if you're careful, and some op amps are very stable, but it's the best suggestion I can come up with.