They are both the same(propanes)... when you put propane gas under pressure it takes a liquid form. This is why your propane tank for your gas grill sloshes around in the tank but when you turn your grill on, it goes from liquid to gas. Liquid Propane "boils" at -45 degrees and turns to a vapor. By putting it under pressure, you kind of "squeeze" the droplets out of the gas and it turns to liquid.

Natural gas is made up of several gases, is hard to compress into a tank and comes out of the ground in that form. It is what gets "pumped" to your house if your community has those underground lines. Propane is easier to compress and put in tanks, it is "produced" and gets delivered by truck to a tank you have stored by your house.