The pre-war power armor suits.
X-02 is seen if Fallout Tactics (and no other game)
X-01 seen in Fallout 4 (and no other game)

X-02 and X-01 where contract prototypes to compete for the government contract in the next step of Power Armor inovation.
Other sources say they where military experiments, but if that was true, than the only military base that would be running major R&D in that part of the US that the mid-US BoS was at would be Scott AFB. Whiteman AFB. or Minot AFB.... all that are AFBs. Because the US Army's major R&D base is located in Maryland.

X-02 took the existing suits and immensely upgraded them.
X-01 looked to make their own all around suit from nearly scratch to supersede previous power armor models.

The X-02 was to be just as easy to manufacture as the T-45D as their primary goal, introduce ultra-light and manuverable aiding servos and components to the suit wile in the end, giving it a sleek nice look. It had improved protections over small arms alot, but fell short against energy and EMP weapons vs the X-01 and even had less effectivness against general explosives vs T-45D.

The X-01 tried to make the 'Tank' to the otherwise 'Mechanized Infantry' of what Power armor was. The X-01 was bulkier, designed to take alot more small arms fire, able to withstand harsh NUCLEAR blast conditions, and be able to still be fixed at a repair point or supply all thanks to its concept material, strontium-90 plating.
Though, harder to make, the armor was much better against energy weapons and explosions. it was able to survive nuclear EMP conditions and not be effective.

Nether contract won due to the Great War.

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Post-war:

X-02 was being constructed by some company in the Mid-US, as thats where it was found by the BoS, and then many years later, found by ED-E then transmitted back to the East Coast for the enclave to upgrade themselves and produce.

Fallout Tactics ends 2198.
APA started up in 2198.
First APA production model made in 2220.
Autumn's father, Autumn Senior, was a high-ranking scientist in the Enclave at the time of its destruction by the Chosen One in 2242. They fled to the East Coast.
ED-E was created in 2275 as a prototype "duraframe" model created in Adams AFB, in the same year, ED-E was tasked with a mission to visit several points of intrest before reaching Navarro on the West Coast. In this time, they did not know that Navarro was lost, just the Oil Rig.
As Ed-E was always transmitting back to Enclave Command. It had to, at some point, send back the schematics of the X-02 that the BoS made along the way, to the Enclave at the time.

This armor would go on to be called the Enclave APA (EAPA) on the East coast with no real designation over X-02.
-

X-01 would be picked up on the west-coast in prototypes. But the Enclave had saved this armor's schematics right before the great war. Full development was restarted by the Enclave in 2198, although it wasn't until 2215 that the research efforts began in earnest under the presidential mandate, resulting in the creation of the first model of Advanced power armor in 2220. This suit base, by far, is the most advanced type of power armor ever made. This armor would go on to be called the Mark 1.
-The Mark II was a further upgrade of the Mark 1. Introducing more well crafted lightweight plating. Its fittings, armor, and servos all round where updated, making the suit 5lbs heavier overall. It had better small arms protection, better direct energy protection, and better explosion resistance ontop of what it already was. The suit remained the same in looks but further pushing as the best armor ever made by man.

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TL;DR

Well. X-01 and APA (Mark I) are different armors,
Mark 2 APA is the same in looks as Mark 1, but composed differently.

X-02 and X-01 are not similar to their baseline makeup.
one is stronger than the other, and one is more agile than the other (X-02 agile, X-01 tanky)

APA Mark 2 seen in Fallout 2 is not Enclave APA as seen in Fallout 3. even though there is some confusion there. Mark 2 is still based off the X-01 baseline. as the Enclave APA is based off the X-02 baseline.