Of course you can make your own pizza sauce, and you likely will want to if you are going to the bother of making a pizza at home (as opposed to ring and bring.) But when you encounter a non-pizza recipe calling for pizza sauce, chances are that what is meant is a store-bought, tomato-based pizza sauce that would come in a can, jar or squeezable bottle.
The squeezable bottle option is a particularly good one. Oftentimes you are faced with a call for “2 tablespoon pizza sauce”, and it is vexatious when you have to open a can just for that diddy amount.
Definitely use the store-bought sauce when teaching kids how to make pizza from scratch. Let them learn the basic principles, and when they’ve mastered those, you can move them onto making the sauce from scratch.
Ketchup or small can of tomato paste mixed with a little water, garlic and herbs (fresh or dried) such as basil, parsley, oregano.