Registrar, nameserver, zone
The registrar records who owns the domain and which nameservers are authoritative. The nameservers hold the zone file. The zone file holds the records. Changing hosts usually means changing the second, third or fourth of those, and confusing them wastes hours.
The records that matter
For a typical site:
- A or AAAA pointing the root at your server
- CNAME for www
- MX for mail
- TXT for SPF and verification
Why propagation is not the server being slow
Every resolver caches your records for the TTL you set. Lower the TTL to five minutes a day before a planned move, and the change appears almost immediately. Leave it at 24 hours and some visitors see the old server for a day.