Does urn-, url-, and uri-encoding all refer to the same thing?

Can someone clarify if URN, URI, and URL encoding are all infact the same thing?

What term is most correct to use?

Yes, they all refer to the same thing. The encoding was originally defined in RFC 1738, section 2.2, and hence called "URL encoding". The URN RFC (2141) also defines that encoding, in section 2.3.1. According to RFC 3986, the correct term is typically URI (especially when talking about the general thing). This RFC defines the Percent-Encoding in section 2.1.