It seems that both armies are made up of battle droids.
Are they the same?
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The Trade Federation Army from Episode I added the support of the Techno Union army and others to create the larger Separatist Army. The Trade Federation Army - a stand-alone army in Episode I - becomes a subset of the larger Separatist Army in Episode II.
Obi-Wan Kenobi witnesses the meeting between Separatist leaders to discuss Dooku's treaty and the formation of the Separatist Army, which they refer to as "the finest army in the galaxy."
good question here. First off, the answer by @TheIronCheek is correct, I just noticed you didn't hit the "question answered" yet, hence why I believe you're looking for more details which I'm willing to give you:
Spoiler warning from this point onwards:
Darth Sidious makes up with the Trade Federation prior to the events as displayed in Episode I. He directs them to do his bidding and promises, in exchange for this, that they'll end up with advantages, supporting their business. Whilst having all those battle droids and Lucrehulk spaceships, they are not fit to fight a war against the republic solely on their own. Thats why Darth Sidious sends out Count Dooku, a former Jedi, to form the separatist movement - commonly known as the CIS:
C - Confederacy (of) I - Independent S - Systems
Hes doing this by influencing systems to break with the republic and by promising positive results to the main factions, to actually form this movement. The main factions as by the start of the war are:
Trade Federation (Ressources) Techno Union (Technology, such as the super battle droids) Banking Clan (Money)
along with all the minor planetary / system bodies and parties, they form the CIS.
So the forces of the Trade Federation ARE part of the CIS forces, but make not up the entire CIS forces - so your answer is no, they are not the same thing, one is part of the other.