Using telnet you run a shell (terminal session) at some other remote Internet site. Logging into a remote site via telnet looks much like logging directly there. Telnet sites are reference either by site name or numeric ip address.
Gopher is a text-menu-based, Internet information service. Gopher provides a more automated way to get information from the Internet than ftp or telnet. I think of gohper as a text-based precursor to WWW. As a point of reference the number of gopher sites is growing at something like 100% a year. The number of WWW sites is growing about 9000% in the same period. A practical note: since they are purely plaintext-based (and less popular), gopher sites are sometimes faster than Web sites.
On a UNIX system you can start gopher from the command line by typing "gopher sitename". WWW browsers also talk "gopher" automatically. Gopher WWW URLs look like: "gopher://". Actual gopher programs (separate from Web browsers) may offer a more correctly structured approach to gopher, especially when it comes to seeking out gopher sites in general.