Why can't I select both of these?
I don't know exactly why the interface is limited and possibly counterintuitive like this. I'm ready to chalk it up to reducing complexity and adding sane defaults. For a desktop user, that often makes sense. However, if you are using a server, you wouldn't be using this method, and so I'll add some info on alternatives that provide more flexibility, at the expense of complexity. They also provide you (given a little time to familiarize yourself with them) a clearer view of exactly what actions will take place.
On the server side, the standard way to configure this is probably to use unattended-upgrades. This might be the best way to do this on the desktop as well.
Here's a decent guide on this (and some other Ubuntu methods): https://help.ubuntu.com/community/AutomaticSecurityUpdates
Note that this guide does not discourage using the Gnome Update Manager, which is GUI you are referring to. This is a user-editable wiki page, so I'm chalking this up to conflating server and desktop tools. (Though it is of course possible to install, e.g., Gnome on a server, too.)
Another method mentioned is cron. Cron has the advantage of being pretty transparent in what it does, and giving you great control, as it is typically hand-configured. This unfortunately also has the consequence of maintainability being limited to whatever system you create yourself.
An older but still available method is to use cron-apt. I've used this on Debian boxes, and it works on Ubuntu as well. I think the documentation is horrible, however.
cron-apt can optionally email status and updates. Here's an example:
A short but helpful page on cron-apt can be found on the TurnKey Linux Automatic Security Updates page. The descriptions work here because TurnKLey Linux is based on Ubuntu. Their cron-apt usage updates more aggressively, about which they have this to say: