To save money, you can have more than 1 domain on a single hosting plan, this means that each domain will have a folder on the server and putting any files in that folder for you websites will load those different websites accoridng to your files.
Now I'm going to explain to you the process of registering additional domains from HostGator.
Once you buy a domain by itself it will come with a settings page, you can set 2 servers in that settings page to the same servers at your hosting plan, this means that once you create a folder with the same name as your domain on your server inside your hosting plan, and put your websites files in there, you will be able to use this folder as your main folder for your websites.
To register addtional domains from HostGator, you must go to their registry website, this is a website that offers domains only, you will not be able to purchase hosting plans from that website.
Step 1:
Enter any desired name you want for your domain and choose the format (.com, .net, .org) then click register as displayed below:
Step 2:
You will be taken to this screen where you can either purchase more extentions or you can select different suggestions from the names they provide below:
Step 3:
Once you fill out all your personal information below you can click register and you will own this domain: