What you describe is called a Virtual Terminal aka VT
Most distributions support switching to a different VT with Alt+F1 , Alt+F2, etc
A graphical environment (X-window) is just one of those VTs, often 6th or 7th.
To switch from an X-Window session to another VT you need to press Alt+Ctrl+F1, e t.c. (unless this is forbidden through novtswitch
option)
I don't remember bare F1, F2, etc ever switching VTs, but you can make them behave like that. Enter following from a root text VT (X-window terminal emulater won't do):
#loadkeys
keycode 59 = Console_1
keycode 60 = Console_2
.......
keycode 69 = Console_10
Press Ctrl+D to finish input
To reapply those changes on reboot, save above to a file and refer to your distro documentation on keymaps, such as this page on ArchLinux wiki