gvim is a simple way to invoke a GUI version of the vim editor. In nearly all installations, gvim is simply a symbolic link to the vim binary, which checks the name by which it was invoked to determine which functionality to use. Running gvim is exactly the same as running the vim binary with the "-g" option.
However, vim is sometimes packaged in several versions, not all of which have the GUI capability. Packages vim-tiny, vim-basic and vim-nox are available on Debian systems, and are compiled without GUI support. Their executables are vim.tiny, vim.basic and vim.nox respectively and are listed in order of increasing functionality.