Yes. DNS records can send website traffic and email to different services.
The website usually follows A, AAAA, or CNAME records. Email delivery follows MX records, with TXT and CNAME records often used for sender verification and mail security.
Before changing nameservers or DNS, copy the working records for every service. Replacing nameservers without recreating the mail records can stop incoming email even when the website works. If you are unsure which provider currently hosts DNS, ask support before changing it.