I don't know which is more appropriate to use, "dig" or "dig up" when both of them mean the same.
Answer from a Native speaker
Oh, well! It can also depend on the context. "Dig up" can mean specifically dig something out of the ground, which is why "up" is used, because it's moving in an upward direction out of the ground. This is sometimes used with digging holes since you're still "digging up" dirt from the ground. "Dig" means to move the earth with tools. It doesn't imply removing something from the earth. Ex: Let's start digging the hole for the swimming pool. Ex: We dug up so many old artifacts! Ex: Moles like to dig holes to move around underground. Ex: I hope my dog doesn't dig up the flower bed again.