The definition of “hosting” does not describe a particular service, but a set of services which provide various functions to a domain name. Having a website and emails, for example, are two separate services though in the general case they come together, so a lot of people see them as one single service. The truth is, every single domain has a couple of DNS records called A and MX, which show the server that manages each specific service - the first one is a numeric IP address, which identifies where the site for the domain name is loaded from, while the latter is an alphanumeric string, which shows the server that deals with the e-mails for the domain. As an example, an A record can be 18.104.22.168 and an MX record can be mx1.domain.com. Whenever you open a site or send an email, the global DNS servers are contacted to check the name servers that a domain name has and the traffic/message is first forwarded to that company. In case you have custom records on their end, the browser request or the e-mail will then be sent to the correct server. The reasoning behind using separate records is that the two services use different web protocols and you can have your site hosted by one service provider and the e-mail messages by another.