What is the difference between screen-256 color and xterm-256color

Solution 1:

tmux is a terminal emulator, since each pane must behave as a separate terminal; its emulation is not exactly the same as that of xterm or gnome-terminal, for historical reasons (it instead matches screen, which predates most of the GUI terminal emulators). It therefore requires a different terminal description to behave properly.

Setting $TERM manually is usually a bad idea specifically for this reason; it will usually be set correctly by itself, with some exceptions usually related to compatibility (older Solaris doesn't understand xterm-256color, for example).