It's all a matter of safe and appropriate parts for planned and possible usage.
In the case of your inverter wiring, you might be putting 50 amps through the wire. In the case of a 12V outlet, it's got a 15 amp fuse on it, so we don't need to provision for more than 15 amps.
16 gauge is safe for 15 amps and with the fuse we don't need to worry about the possibility of putting more current through it. But depending on your planned usage it might not be appropriate -- it provides enough resistance that you get enough voltage drop over longer runs that some inexpensive inverters will fail.
2013 Escape 19 ("The Dog House") , 2012 Nissan Frontier