No, CNAME and NS are quite different.
CNAME associates an alias with a canonical ("true") name. So in your example,
dns.mysite.example would be an alias for canonical/true name
mysite.example, and all DNS queries for
dns.mysite.example would be referred to (ie, retried with)
NS records identify an authoritative name server for a domain (more correctly, a DNS zone). They tell a DNS query where to look for authoritative detail about a domain (zone). Typically, unless you are setting up name server infrastructure, your domain registrar will provide correct NS details for your domain (typically, a few name servers for redundancy, each controlled by your registrar, such as
For subdomains which will resolve to the same address, you do have a choice between A and CNAME records. The practical difference between A and CNAME records is that CNAME will cause an additional lookup (to resolve the alias to the canonical name) which is not incurred with a direct A record. So there is a slight performance penalty on lookups if you use CNAME records rather than individual A records for your subdomains.
The root zone file does not contain any CNAME records, but that's not because it can't, but that it doesn't need to. It mainly contains NS and address (A & AAAA) records for top level domains, for country-code top level domains (and, more recently, for all those new/extended TLDs like .auction).