A VPS is a virtual private server connected to the internet that is running on a larger, real server.
Webhosting is renting (space on) a computer connected to the internet, on which you can run a website.
WordPress.com is WordPress as a Service. At WordPress.org you can download WordPress to use at your own hosting.
WordPress is a so called Content Management System. With WordPress, you can easily build a website and add content yourself.
Transactional email is sent automatically as a result of a transaction on usually an app or website.