A domain name and hosting are two separate things. If you want to host your own website, you usually want both though, so they are sold as a package.
Hosting is a piece of hard drive on a computer that's online 24/7. It's where you upload your website files, so they are always available for viewing. Since those computers have really long, ugly web addresses, you also get a domain, then point it at the hosting.
Think of it like this: hosting is the actual house, it's where you put your furniture and your clothes and your stuff (i.e. the website files). The domain is the street address you tell your friends, so they can find your house.
Wordpress needs PHP support and a mySQL database. Since those two are the most common choices, 99% of hosts offer those in their basic web hosting plans. Those plans usually come with a free domain on top.
To set up Wordpress, you can either use the "one-click installer" in the host's admin interface, or you upload Wordpress yourself and set it up by visiting your domain.
Wordpress hosting is a plan specifically geared to host a wordpress site. It's usually a bit cheaper, but it only supports Wordpress.
TL;DR:
Compare Wordpress hosting with the cheapest standard hosting, and pick which ever is cheaper.
As an example, basic hosting from 1and1.com is 0.99/month the first year, then 6.99/month.
Their basic wordpress hosting costs exactly the same but limits you to a single wordpress installation.
So here I'd pick the general hosting plan, because you could add a 2nd domain and run a 2nd wordpress website on the hosting plan you already have.