In 2003 Wordpress was launched as a free blogging platform, however, later it evolved as a content management system. If you want to use wordpress, you cna use it in two ways, one as a blogging platform (free and premium), two content management system to create any kind of website you want (blog, business website, online store, etc.
Wodpress as a blogging platform
If you want to use wordpress as a blogging platform, you can go to wordpress.com, sign up and launch your blog just in a couple of minutes. There are two options to choose, one a free blog, two, a paid blog. Free blog will get you a subdomain (yoursite.wordpress.com), premium service will give you a blog with a custom domain. When you choose premium option what you are doing is hosting your blog with wordpress hosting
Wordpress as a content management system (CMS)
When you are using wordpress as CMS, you can create wordpress site locally by downloading from wordpress.org. You don't need a domain or hosting to create locally, however, if you want to make your site live, you need hosting. If you have hosting account, you can directly install wordpress on your server through Cpael
Wodpress as a blogging platform
If you want to use wordpress as a blogging platform, you can go to wordpress.com, sign up and launch your blog just in a couple of minutes. There are two options to choose, one a free blog, two, a paid blog. Free blog will get you a subdomain (yoursite.wordpress.com), premium service will give you a blog with a custom domain. When you choose premium option what you are doing is hosting your blog with wordpress hosting
Wordpress as a content management system (CMS)
When you are using wordpress as CMS, you can create wordpress site locally by downloading from wordpress.org. You don't need a domain or hosting to create locally, however, if you want to make your site live, you need hosting. If you have hosting account, you can directly install wordpress on your server through Cpael