Just a couple of comments from italy
From what i can gather,after 35 years here, battuto is what they call it in rome and it usually means chopped up pork fat in with the onion, etc.
"Battuto" comes from "battere" meaning beat, the origin probably being the knife bangs on the board to cut it all up
Usually "soffritto" means literally "under-fry" like "sobollire" means "under-boil" or simmer
I think they are pretty interchangeable and the terms are regional preferences
.
I never had a bolognese in bologna, and i assume every family in bologna has its own version, like everything else. However the "Accademia Italiana della Cucina e l'associazione Confraternita del Tortellino" (which (get this) means italian academy of cooking and the confraternity of the tortellino) has registered ragu alla bolognese as a historically important recipe with the chamber of commerce in bologna.
the beef is supposed to be from a part of the animal near the stomach which is particularly fatty. I'll translate the recipe i found which claims to be the traditional one.
However, notice that a major problem with american presentations of pasta, is that an italian would never serve the pasta with the sauce on top, but the sauce must be mixed with the pasta as soon as you drain it, or it gets all sticky and disgusting. This keeps the pasta separate.
Here's the traditional recipe for 4 portions (sauce alone has 700 calories per serving.
300 grams of this beef mentioned above called "cartella", ground
150 grams of unsmoked and unsalted fatty bacon meat (pancetta dolce) minced
1 carrot
1 celery
1 onion (each about 50 gm)
5 spoonfuls of tomato paste mixed with a ladleful of broth
1/2 glass of white or red wine
200 grams of whole milk
melt the bacon in a pan. Add the finely chopped vegetables and let them slowly get soft. Add the ground meat and let it cook, mixing occasionally, until it gets slightly browned. Add the wine and the tomato paste mixed with broth and let it simmer for 2 hours, adding milk a little at a time, and seasoning with salt and black pepper.
If you like you can add at the end, about a half a cup of heavy cream.
Most people today make it with lean beef and pork, and use tomatoes not paste, and no milk or cream. It's those calories that they try to eliminate.