All the LIPOs has 3.7 V, but different currents, what is the difference? For example: If I connect a module that use 3.7V each LIPO can give the sufficient power to my circuit without burn it out?
Yes, all the LiPo's have a nominal voltage of 3.7v (though it's actually as high as 4.2 when fully charged - but most of the discharge curve is ~3.7).
There are two other specs commonly given:
Capacity, in mAh - milliamp hours (also sometimes given as Ah - Amp hours). This is the rated (ie, wildly optimistic) capacity of the battery. If I have a 100mA load, and I connect it to a 500mAh battery, it will (theoretically) last 5 hours, whereas a 1000mAh battery would last 10 hours.
Discharge rate, in amps or mA - the maximum current that can be safely drawn from the battery. This is a peak current, and you generally want a battery capable of supplying a lot more current than you intend to use (some batteries are spec'ed with max peak current and max continuous discharge). This is sometimes given in "C" rating; 1C is a current sufficient to exhaust the rated capacity within 1 hour - ie, 1C on a 500mAh battery is 500mA.
If you short circuit a high current battery bad things happen - yuou might add a fuse to protect the wiring
for instance.
If you don't short it out, 3.7V is 3.7V, if the circuit is happy with 3.7V it doesn't matter if the
supply can provide a hundred times more current than is needed, the circuit just takes the
current it needs.
Things are absolutely that simple - large decoupling capacitors can mean large inrush currents
flow when the battery is first connected for instance.