Citric acid, and lemon juice are commonly used to can tomato sauces/paste. Older canning recipes use vinegar instead of the citrus option. Both options have salt added as well.
A fresh sauce can be made by dipping fresh tomatoes in boiling water, taking the skins off, squeezing out the gel/seeds, and cooking down the tomato flesh, into a sauce. You can make it more interesting by sauteing chopped onions in oil, adding thyme (or other herbs) and salt to add to the sauce. A fresh sauce does not need an acid added since it isn't being canned. Fresh sauce can be acidic all on its own. A pinch of baking soda will take off the acidic edge.
Another option is to take dehydrated tomatoes, ground up, and add water to make a paste. No citrus added.
I usually make tomato sauce by cooking down the entire tomato and blending it with a hand blender. A hand blender will demolish the skin. To remove the seeds it can be put through a mill (or not). I hope that helps.