In this context they mean the same. "Reach" actually means "to arrive" but it suggests that it was with some degree of difficulty.
For example:
After a month of travelling I finally arrived in Mongolia.
After a month of travelling I finally reached Mongolia.
So they mean the same but the first sentence is just stating a fact they they arrived.
But when you use reach in the second sentence it is a bit charged emotionally as well, tye journey was long and difficult and you emphasize that you finally managed to get where you wanted.
Hope that helps ;)