How does a 700W PSU deliver so much power when most wall sockets are limited to about 20 amps?
Yes it is correct.

The power supply converts power with small losses. So IV formula on both sides with respectable voltages.

Because of the mentioned losses it would draw more than 700W from the outlet (~750-800W I would expect for an decent power supply).

So for 800W on the input it translates to ~7A (in US).