The distinction that causes the most confusion: a lookup returning nothing is usually not an error. DNS separates two very different outcomes, and conflating them sends people looking for problems that do not exist.
NOERROR with no records means the name exists and publishes nothing of the type you asked for. Perfectly normal — a name with an A record and no TXT record is the common case, not a misconfiguration.
NXDOMAIN means no zone covers the name at all. That is the genuine error: the domain is unregistered, expired, or misspelled.
Why answers disagree between tools
Every resolver keeps its own cache and holds each answer until the TTL runs out. Right after a change, this tool and your local dig can legitimately return different results for hours. The TTL column tells you how long the stale answer may persist, which is why lowering it before a migration and raising it afterwards is standard practice.
For mail specifically, the dedicated tools give more than raw records: the MX lookup resolves each exchange and reviews the configuration, while the SPF checker and DMARC checker parse the TXT records those policies live in rather than just printing them.