Sauce – What kind of sauce did I “invent”

The reason that your basting sauce flopped was the recipe was calling for an emulision (basically, a vinegrette) and by leaving out the vinegar you are changing the one of the basic building blocks of the dish. The sauce will require that you add the fats to the mustard as it will clump as experienced if you don't. The mustard in the original recipe is used as an emuslifer and may need to be cut down without the addition of the vinegar. To build a sauce like this, you should start with the vinegar, add the seasonings and any emulisfers (in this case, the mustard) and slowly drizzle the fats into the resulting mixture until all has been incorperated. You will still get a smooth sauce as long as you keep the order even if you leave off an ingredient or two.

Pizza sauce is, presumably, whatever tomato-based sauce you'd put on a pizza. Those tend to be essentially like smooth (not chunky), lightly seasoned spaghetti sauce. If by "plain tomato sauce" you mean a jar of tomato sauce for spaghetti, you're probably in good shape. If you mean a can of pure tomato sauce, with no other ingredients, you'll probably want to add some seasoning. Basil and oregano are good bets for herbs; garlic and onion are also common, and perhaps crushed red pepper if you want a little kick.

If you're looking for a real recipe, this isn't a recipe request site, but search engines will serve you well.