Both are correct and similar but I would use them differently. “Go right” is similar to “turn right”. But if I’m giving instructions of what to do when you come to a fork, “go to the right” is similar to saying “take the path on the right”. It might not involve much of a turn at all. When you get to the cathedral... “Turn right” (clear, turn 90 degrees, keep going) “Go right” (not as clear as “turn”, but by default I would treat it like “turn”) “Go to the right” (a little unclear but by default “go around the cathedral on the right side”)

Thank you Chris

"go right" and "go to the right" are both correct. "go right" is much more common.