An "A Record" Returns an IP address, most commonly used to map sitenames (ex. directory.yourdomain.com) to an IP address of the host, but also used for other things.
So in simple terms, an A Record just assists in telling your computer where to go when you view someone's website, or sub-domain.
If you had the domain: npjbe.com and the server's IP that your domain was on was: 55.555.55.55
then the A Record you would create for npjbe.com would be point to that IP (55.555.55.55).
If you wanted to point your domain to another server other than the one you are currently on, you would tell the A record to link to the other server by entering that other server's IP.
So, no, an A Record and IP Address is not the same thing, but they work side by side with each other.