Honestly, the battle droids and general evilness alone should be enough to connect the Separatists and the Trade Federation. Both organizations are hilariously generic in the sense that we learn practically nothing about their precise motivations. All that is given in the movies is that the Trade Federation doesn’t want to pay taxes because they are greedy, and the Separatists? Well, they are characterized by their dislike for the Republic and the Jedi. Based on the abundance of big companies present at Dooku’s meeting, we can infer that they share the same bland motivation as the Trade Federation, money.

So, I think the distinction between the two can be put in the crawl of ROTS, without losing anything.

Actually, the bigger question is why Dooku is on their team. His supposed motivation to leave the Jedi and the Republic is the corruption of the senate, but the first thing he does after leaving is founding the League of the Uber-corrupt, super-capitalist of the galaxy. It just doesn’t make any sense. I mean, what greater good could justify this absurd action against his actual beliefs?