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”)