There's no real difference, coppa and capocollo are synonyms. We call this cut also "ossocollo" (neck bone) where I live (Veneto, northern Italy). Other regions call it with different names; for a full list please check: https://it.wikipedia.org/wiki/Coppa_(salume)
Coppa (aka capocollo) is a type of cold cut (salume) in Italy. You'll see it with different names, including capocollo, lonza, and lonzino. They are all made from the same part of pork. It comes from the neck to the fourth or fifth rib of the pork shoulder or neck, and the name "capo-collo" means "head-neck." "Di Parma" simply means from Parma, and it means the product is created according to certain traditions from that region (though it's actually produced in other regions). The word "coppa" means "cup" in Italian. I'm just guessing here, but I suspect it may be called this because of its shape which is created when it is trimmed (it is cut to be cylindrical).
I suspect the two products you are looking at have different amounts of fat. They are probably both delicious.
There is some ambiguity about what is called what, and I don't have information about how these words are used in Italy, but in my experience (in Italian delicatessens in the Chicago area):
Coppa is a dry-cured salume from the neck of the hog, is pressed, so has a dense texture similar to prosciutto, has a dark maroon color, and is about 6 or 7 cm in diameter. https://www.volpifoods.com/products/sliced/traditional-coppa-3oz/ Capocollo is a cooked salume from the shoulder, has more of a ham texture and a pink color, and is about 10 cm in diameter. https://www.volpifoods.com/products/sliced/uncured-cooked-capocolla-4oz/
Both come in mild and hot (spicy) versions.