"Go to work" implies that somebody is telling you to leave where you are at the moment and go to where your job is. "Get to work" implies that somebody is telling to start working on something that you were not doing in the moments before.

Hello Kou, They are not the same. 'Go to work' is when you leave the place you live to travel to work and 'get to work' is when you arrive at the place where you work. Hope this helps Bob