I make both (don't have Italian sausages where I am). Pork butt cut in chunks for sausages, ground beef for meatballs.
Sausages use a curing salt (gives them a pink color, otherwise they'd turn gray). I let mine sit overnight before grinding/filling. Not as many spices in sausage. For Italian I use fennel, garlic (fresh), salt pepper, maybe a little oregano, and red wine vinegar along with the curing salt. Keep overnight in fridge with ice cubes. Meat should be slightly frozen before going in the grinder.
Meatballs have more spices (basil,thyme, parika etc.), plus an egg and some bread soaked in milk. Mix up room temp and form without sitting overnight.