[ubuntu-uk] Difference between Admin and Root?

[Mac]

I have a single-user system, and - while playing / investigating - I 
tried changing my user password.  I was interested to notice that this, 
rather than root's password was then the one required by 'sudo...'.

I suppose I'd sort of expected that 'sudo' would require the root 
password, and that when needing to act as root (e.g. to use aptitude) 
I'd been typing the root password, which just happened to be the same as 
the first user on the system, but wouldn't be if that user changed 
his/her password.

So what's the difference, if any, between a user invoking his/her 
'Admin' rights with the 'sudo' command, and what root can do?

Would it be possible / wise (for reasons of security) to remove the 
admin rights of the first user on the system, leaving root as the only 
user with such rights?  (I'm inclined to think not, having set up a 
second user without admin rights on another system, and noticing that a 
number of 'administrative' menu options did not then appear in the menus.)

(Not a big issue - just interested in learning more about GNU/linux from 
you guys who know!)

Mac