If they delegate it to a nameserver you specify, is it much different to a domain? I am assuming they delegate in this manner, as opposed to some free web host

If they delegate it to a nameserver you specify, is it much different to a domain? I am assuming they delegate in this manner, as opposed to some free web hosts who would host the nameservers and essentially just let you set A records. Would you say that example.nsw.gov.au is a domain or a subdomain?