As Paul mentioned, domains and email hosting are two completely different things, but they are closely connected.

A domain name can be purchased through a wide variety of companies, often referred to as Registrars (you’d be the registrant), and once you have that domain you can effectively do whatever you like with it.

Associated with the domain name are DNS records, and they’ll generally (not always, but that gets more complicated than need be) be hosted by the Registrar that currently provides the domain for you. The domain belongs to you, so you can choose down the road to transfer it to a different Registrar, after which they’ll handle things like renewals, your DNS etc instead. It’s not tied to any one company, it’s yours (for as long as you keep renewing it!).

The DNS records include things like A records pointing to websites, MX records pointing to email, and a variety of other possible services. That’s why there’s no such thing as a “web domain” or “email domain”, they can be either or more commonly both.

With things like email, the MX records tell the internet that anything @example.com should be sent to x mail server. Then the mail server handles what to do with [email protected], info@, sales@ etc.

You could have your domain held by one company, your email services held with another, and your website with a third, or all three at the same place. You simply get the relevant DNS records updated to point to the appropriate destinations for each service, with the provider giving you detailed instructions of what to change where.

In the specific example of Namecheap, those packages are specifically related to the email service, not to the domain name. Note near the bottom of the page in the FAQ under “How do I get a company email address?” it specifically talks about the option to purchase the domain through them, but that if your domain is currently held elsewhere you can still use it with them, eg it’s not an included part of that service but an available extra. What they don’t spell out (I imagine it’s covered in their documentation), is that if the domain was held elsewhere then you’d simply get the email related DNS records setup to point to Namecheap’s mail servers to get it to work.

Finally, you mention “use that domain to link my IP to host on my local PC a web server”. Technically yes in theory, but there are a LOT of catches which unless you’re a lot more experienced with how that kind of thing works I wouldn’t even attempt it. There are plenty of cheap web hosts available that will provide web hosting services (including many of those who provide email hosting).

Note, even this long reply is quite generalized, but hopefully it explains the concepts involved.