XTerm instead of Terminal in .desktop
.desktop and the Ctrl-Alt-T shortcut all launch x-terminal-emulator , which is a symlink to /etc/alternatives/x-terminal-emulator , which in turn is a symlink to /usr/bin/gnome-terminal.wrapper. In short, gnome-terminal aka Terminal is the default terminal emulator on Ubuntu.
If you want to use xterm for just one .desktop file , follow muru's suggestion in the comments and use use
Exec=xterm -e /path/to/script.sh
If you want to globally change the terminal that the system launches by default, run
sudo update-alternatives --config x-terminal-emulator