The local Administrator account and a domain account that is a member of the local Aministrators group. How to simply describe the difference.

Interesting question. The local Windows administrator account has rights to do anything on the local computer but nowhere else.

A domain account has rights across the domain and potentially on multiple computers.

I'd say there is no difference in practice as to whether a task is performed as a local Windows administrator or a domain account that is a member of the local administrators group.  

Using the local Windows administrator account could be a problem on a network with large numbers of computers in terms of keeping passwords the same whereas with a domain account only one password is needed.

Why do you say that the local administrator account is better?

In practice it's better to disable the local admin accounts (and rename them), since they can be messed with if someone has access to the computer. Using a domain account as a member of the local admins group is the way I'd go. Not sure i'd recommend using the local admin account to work on a domain computer.