What is the difference between pizza sauce and spaghetti sauce?
Red pizza sauce is often (but not always) two things:


Thicker.  Thinner sauce will tend to run in the oven and also steam the pizza crust as it cooks - if loaded with toppings, otherwise thin is fine.  Depending on the crust, the heat of the oven, the toppings above sauce, and how watery it is, this may not be needed.  If you've just got some crushed tomatoes and a few bits of cheese in a super hot oven - the sauce should be fine without reducing beforehand.  If you've loaded up a bucket of sauce and a pound of cheese, precook and reduce the sauce.
It's often simpler.  Many pasta dishes like spaghetti highlight the sauce and hours of simmering happen for the sauce to bring it to perfection.  They're all about the sauce.  Pizza is really about the crust and what highlights it.  Many of the best pizzas are simply topped.  Crushed san marzano tomatoes (sometimes) reduced with a hint of salt is often all I do, and franky, it's enough. I'm not talking about the jarred varieties here, but what you might cook at home.  Jars in the store, the main difference is just how thick it is.