Start with the name
A domain is an address people recognise. Registration gives you the right to use an eligible name for a term, subject to registry rules. It does not create a website or mailbox by itself.
Then decide where the website lives
Hosting stores the site’s files and database. DNS connects the name to that hosting account. Moving a website therefore involves both a tested copy and an approved DNS cutover; the two should not be confused.
Mail has its own route
Mailbox hosting provides the accounts, authentication and delivery route for email. MX records connect the domain to that service. SPF, DKIM and DMARC support authentication, but do not magically guarantee delivery or replace an anti-abuse policy.
Keep ownership and renewal visible
The customer should remain the domain registrant. Check registration, normal renewal and transfer terms separately, and understand whether licences are annual prepaid. A convenience bundle groups the discussion; it does not make any component free.