Two different UIs confuse people: the registrar’s “change nameservers” screen, and the DNS host’s “edit records” screen. Records you add at host B never go live if the registrar still delegates to host A. An NS lookup is the tie-breaker.
Glue
If you want ns1.example.com to serve example.com, the TLD must also publish the IP of ns1 — glue — otherwise a resolver cannot find the nameserver without already knowing the zone. Registrars expose this as “register a nameserver” or “glue records.” Get it wrong and the domain looks dead even though the DNS software is fine.
How many
Two is the minimum for any serious domain. Four is common. They should not share a rack, a network, or a single cloud region if you can help it. Changing NS is a high-TTL event; treat it like a migration, not a typo fix.