You need to do this through System Prefs rather than the Mail App.
Mail itself will, strangely enough only deal with mail and nothing but mail!
If you go though
System Preferences -> Mail aAccounts etc... -> Add/remove
That is where you can set up their existence. This includes all calendar, notes etc... accounts.
Just to add, if you're new to apple:
Click on: logo, top left of the screen,
System Preferences in the menu
In there you'll find mail etc....
Embarrassing as it is to admit, I have been a long time Apple user, but in the past couple of months my email has started to disappear, sometimes right in front of my eyes the moment it arrives to the inbox.
In any case, are you saying that I should not add my different email accounts in the Mail app account settings? How would I go about assigning email signatures if I only use the system preferences settings?
Apple support article on account setup for Mail.
When I set mine up I did the accounts in Mail and they then showed up in System Preferences. There is no way in System Preferences/Mail, Contacts & Calendars to set up the server settings for example.
You can set your signatures in Mail/Preferences/Signatures.
To answer the OP's original question.
Both the System Preferences -> Mail, Contacts and Calendars AND the Mail.app -> Accounts route both take you to the system preferences pane.
Just so you can confirm it, try both methods to get to the accounts list, and at the top left of the particular window you'll see 'Show All' which takes you back to System Prefs.
I think it's just apples way of getting everyone to the right place i.e. those who are use to using system prefs and those who are used to setting up accounts in their mail apps
That's good old apple and their user friendly interfaces for you