Looking at the packets in Debian, there are two different implementations of netcat (
nc), I think both of them install with
netcat as well as
nc symlinked to the same binary (Though they use Debian's "alternatives" system to control which one of the implementation appears with the main name.) Those two are
netcat-traditional ("the "classic" netcat, written by Hobbit. It lacks many features found in netcat-openbsd.") and
netcat-openbsd ("the OpenBSD rewrite of netcat, including support for IPv6, proxies, and Unix sockets.").
ncat is the version of netcat from the Nmap Project claimed to be "a much-improved reimplementation of the venerable Netcat".
All three seem to have the same basic functionality, as in being able to open a socket and connect or listen, but for anything above that, you may want to check the manual of your version. (The OpenBSD one doesn't support
-e for executing a command after connection, for example.)