What’s the difference anyway?

I would look at it in terms of a main dish (spaghetti sauce) vs. a side dish (pizza sauce). When you order Spaghetti or any type of pasta with a red sauce the featured ingredient is the sauce, this is where the flavor of the dish comes from, depending on your taste you’ll usually choose the sauce that you desire. For this reason the sauce will be cooked longer, include more spices, and the thickness will be determined based on the sauce ordered.

With Pizza Sauce the flavor is not meant to come from the sauce but instead the toppings you choose, the sauce becomes a lesser ingredient. The sauce may not be cooked before hand but instead just a mixture of tomato paste and tomato sauce with a few or no spices added. In general it tends to be thicker than spaghetti sauce but that depends on the spaghetti sauce.

Spaghetti Sauce should not hurt your pizza assuming it is thick enough and not runny. Depending on the sauce it may add a little flavor to it, but I would suggest going without the sauce and finding a pizza recipe online that doesn’t require it.