An A record is a DNS record that points a domain or a subdomain to an IPv4 address. AAAA is the same, but for IPv6 addresses.

An NS record is a DNS record that delegates a domain or a subdomain to set of nameservers. By default they are set to your current DNS nameservers. Example: Adding an NS record like this:

subdomain NS ns1.he.net.

delegates subdomain.yourdomain.com to ns1.he.net, which allows you to use he.net's DNS service to manage everything DNS-related to subdomain.yourdomain.com and anything.subdomain.yourdomain.com.