vim-tiny differs from regular vim in how much stuff is compiled into it. Regular vim is actually quite hefty since it includes e.g. scripting bindings to Python, Perl, Lua, etc.; or support for X11 (which is useful even in a terminal for working with the X clipboard), and so on. If you have both vim and vim-tiny installed, you can use the command ":version" to compare which features have been compiled in.