These are not the same thing and you really need to go with WordPress.org see here
This can be very confusing for first time users. If you look at the names you would pick the difference is the .org vs .com extension in the name. All site names (Domain names) have a dot something on the end. Domain names can have many different extensions. You will have seen .com, .org, .gov, .edu and many more. The .com suffix was one of the original extensions at the beginning of the internet era. It is known as a TLD (Top Level Domain). Generally it is more preferable to have, and consequently a little more expensive depending where you buy it. Now .org is generally a domain extension used for non for profit organisations. When WordPress CMS (Content Management system) was created by Matt Mullenweg and his co-founder, it was released to the public as open source software. This means it was free to download, use and experiment with. At that point they decided to set up two pathways. One under the .org banner to develop the software and make it available to open source usage. The second under the .com banner where they could offer services in a commercial way. Even a free feed has to be paid for somehow. This also included free hosted sites on their servers with tightly controlled and regulated rules. More control could be purchased buying yearly plans.
So if you want full control of your website you download the WordPress.org software, find a hosting company suitable to your needs, buy a domain name and get started.
How it works
Find a Domain name
You may choose your own domain name but must rent the license to do so first. All domain names must follow proper regulations and fall under certain restrictions, such as being unique and only consisting of letters, numbers, and hyphens. A domain name cannot be bought, but you can keep using it as long as you pay the fees for it.
This is you site name. This is where people find you on the internet. It is also your full address all wrapped up in one. Domain names are tightly regulated by ICANN (Internet Corporation for Assigned Names and Numbers) No two websites can have the identical combination of name and suffix. The name is registered in a central database along with which hosting company server it resides on. When somebody clicks on the name in a search browser the central database converts it to an IP (Internet Protocol) address to find your site. IP addresses are formatted as a string on numbers denoting the region, zone, server information to your site.
The following IP address ranges belong to Google:
22.214.171.124 - 126.96.36.199 188.8.131.52 - 184.108.40.206 220.127.116.11 - 18.104.22.168 22.214.171.124 - 126.96.36.199 188.8.131.52 - 184.108.40.206 220.127.116.11 - 18.104.22.168 22.214.171.124 - 126.96.36.199
Domain names usage can be purchased through a number of companies Consider a hosting company as a huge room full of filing cabinets. You rent the use of one of cabinets. Your domain name goes on the front of the cabinet. Your website software goes inside to manage the drawers. Your content, pages,photos, downloads, shop etc is placed inside the software which stores it in various drawers. Someone searches on the internet, finds your domain, which links to this hosting company which sends them to your cabinet. The software delivers the content from the various locations for people to view and navigate.