What's the difference between "Hack" and "Hack No Key" options?

Hack no key, as the name suggests, will give you no key. You can also achieve this via glyph hacking and signaling 'less' via the control channel, but this is a lot more convenient.

It is quite useful while farming for items, or travelling in a new area you know you need no keys from, but it's good for your explorer badge. Spares you getting rid of the keys later.