TL;DR

A whois query on your name yields:

    Registrar:
        Paragon Internet Group Ltd t/a Tsohost [Tag = UKWEBHOSTING]
        URL: http://www.tsohost.com

A DNS query on your name yields:

$ dig @$(dig NS sch.uk +short | head -1) NS st-dominics-catholic.staffs.sch.uk +noall +auth +nottlunits
st-dominics-catholic.staffs.sch.uk. 172800 IN NS ns23.domaincontrol.com.
st-dominics-catholic.staffs.sch.uk. 172800 IN NS ns24.domaincontrol.com.

Domaincontrol.com is famously base domain used for nameservers by GoDaddy (both a registrar and a DNS provider). Your registrar website should show clearly if those are "its" nameservers (handled internally, because the registrar is a reseller or brand or entity of GoDaddy, who is obviously the DNS provider) or "external" ones. Its support should also be able to clarify the situation.

However a search around yields https://www.wordfence.com/blog/2021/11/godaddy-tsohost-mediatemple-123reg-domain-factory-heart-internet-host-europe/ which says:

tsoHost, 123Reg, Domain Factory, Heart Internet, and Host Europe were acquired by GoDaddy as part of Host Europe Group in 2017

The details in general

There are 2 planes: the registration plane and the resolution plane. They do intersect, but are separate.

When you register a domain, and later on update it, renew it, transfer it, etc. this has to happen through a domain name registrar because, for some exceptions, all domain name registries, aka "owners" of TLDs, never sell direct to end customers but only to registrars. Of course you might not interact directly with a registrar, but one of its resellers, or even a company not being officially a reseller of a given registrar but still using it for its domain name operations.

It is through the registrar that you specify the authoritative nameservers for your domain. The registrar does a single thing with that information: it forwards it to the registry, through specific protocols and channels (typically EPP), so that the registry can then list your authoritative nameservers as NS records in its own zonefile.

The registrar DOES NOT participate in the resolution, aka when someone asks about details, and specifically IP addresses, of any name in your zone. You can not edit content of the zone (records) at the registrar, you can just change the list of nameservers for your zone.

This is where the resolution plane appears, and is controlled by the DNS provider, who is the entity administratively and technically maintaining those nameservers.

Content of the zone (aka records) can only be edited at the DNS provider through the interfaces it gives for that (website, API, etc.). Anyone is free to host and edit the same zone on other nameservers, but it doesn't matter, because those nameservers won't be authoritative on the zone and hence won't be queried by default, so their content is irrelevant.

Of course, a given company can be both registrar AND DNS provider, and even be DNS provider for domain names it is not the registrar for (and of course be registrar for domain names using other DNS providers). It can be seen as a benefit (less actors) or a drawback (more eggs in same basket, bigger chance of catastrophic failure), or both, so it is subjective and there are mitigations in both cases. But even if it is a single company doing both, it is important to understand the distinction between the two.

If you do a whois query on your domain (ideally on command line or on registry website directly, avoid any generic website online pretending to do whois queries), it should show who is the registrar of your domain, and even if you registered it through a reseller, the whois will show the registrar, not the reseller (there are rare cases, .de TLD being one, where a whois query won't show even the registrar. Complain to the registry directly).

whois will show nameservers as well (hence the DNS provider your domain is using), but this is not authoritative. A DNS query for NS record type on your domain name towards the registry authoritative nameservers is what will tell currently what is published by registry as your authoritative nameservers, hence the DNS provider your domain name is currently using.