The distinction matters: NXDOMAIN means the name does not exist at all. If the name exists but not the requested type (e.g. no AAAA), the answer is NOERROR with an empty answer section (NODATA). SERVFAIL means the resolver could not get a valid answer, often due to DNSSEC or delegation errors.
Negative answers are cached for as long as the minimum value in the SOA record says. If you create a name after it has already been queried, you have to wait that long.
Common causes: typos, an expired domain, a record created at the wrong DNS provider, or split DNS that answers differently inside and outside the network.
Example
dig new.example.com | grep status