DNS, email and web pages are all different services and can all three be hosted on the same or different service providers. If you are confused, you could think them through an analogy:
- DNS is like a phone book having information on all the people with their contact information.
- IP addresses on
A records are like phone numbers. You could e.g. have one for your landline, one for your gsm, one for work etc.
- Email service is like a fax. You can tell you have a email service through
MX records, but eventually it's handled by servers with IP addresses. Likewise, a fax machine has a phone number: there's just a mention on the phone book telling it's not a normal number someone would answer.
- If you point your
example.com MX to a different domain
mail.example.net it's like telling you don't have an own fax number, but faxes to you could be send to a fax machine at your workplace.
Now, neither the phone company handling your gsm nor your fax line doesn't have to maintain a phone directory having your numbers, although they both could. Also, anyone already knowing your number can contact you; the service exists to publish this information. The same applies to DNS.