The main difference between processed foods and fresh foods are 1) preservatives and 2) flavour enhancement - for the first goal we use things like salt to increase the shelf life of the product which has the side effect of shifting most folks over to having a higher expectation of salt content in their food in general - for the later salt is also useful (along with specific flavour enhancers like MSG), but sugar is far easier to throw in and get more bang for your buck.

I can cook a meal and freeze it for a while reheat it and enjoy it - to allow it to survive (with a decent taste) long bouts of freezer burn and going stale I need to load that sucker up with a bunch of salt and sugar so that I don't care that the food tastes like cardboard.

I can't speak to any molecular effects - those may also exist - but most of why processed food is bad for you is just to make it taste really really good so you'll come back for more - even if you're not hungry! Yay obesity!

I imagine at some point in the future folks are going to look at the diet of the late 20th century like we look at covering your baby's crib with lead based paint.