Do the color of the wires correspond to the letters on my new thermostat?

There is no code governing wire colors and thermostat connections. The thermostat should be wired by the letters found next to the wire screw terminal block. If you do not know the letter labels, then you can trace the wires back to the air handler/furnace or heat pump/ac unit. That will allow you to determine the function of each wire at the system and then allow you to attach it to the matching terminal on the thermostat.