1. An AddOn Domain - When you create an addon domain via cPanel, the main differences from a "Normal domain" are:

A concern here would be the drive space available to your "Normal domain". That is if you are allocated 100MB for the normal domain and you've created an addon domain then both your normal domain and addon domain share the 100MB drive space. The drive space is determined by your Package. 

b) For example with the Business package you can have both www.yourdomain.co.za  and www.yournewdomain.co.za set each with 600Mb disk space ( two websites one account). 

2. A Sub Domain - A Subdomain looks like: something.yourdomain.com where yourdomain.com will obviously be your domain. The content for a Subdomain is served from a folder inside your domain's user directory, for example:

A few uses for subdomains:

You can set 'forums.yourdomain.com' to serve files from a specific directory on your site: '/home/username/www/forums' so that you can use the subdomain in your browser 'http://forums.yourdomain.com' instead of typing 'http://www.yourdomain.com/forums/'.