Today's review said Wolverine's costume was changed to be the same in all continuities. Let's take a look.
Here, via HalloweenCostumes.com. is what all three Wolverines were wearing at the time: 616, Ultimate, and Animated.

Okay, good, three distinct looks.
What Marvel calls his "combat" suit first appeared in Uncanny X-Men #423, released May 5, 2003. Because that issue's cover is not great, here he is as seen on the cover of Exiles #28 (June 4, 2003):
Here's the cover of Ultimate X-Men #33, released July 9, 2003 (although he wouldn't start wearing this new look until issue #39, four months later):
Those both appear to be based on Wolverine's Season 3 redesign in X-Men Evolution. The first episode with it aired September 21, 2002, but given how long animation takes to produce, it would have been designed and approved at least a year earlier.

That means the design, shared between all three Wolverines, was clearly based on the Adam Kubert art used for the variant cover of 2000's Uncanny X-Men #381, which was itself an attempt to adapt the movie costume:

Black suit, yellow lines on the shoulders... it's not the same thing, but it's undeniable what they were going for.
The idea behind making them identical was one of expediency: if every version looks the same, then any cool piece of art can be used to promote anything you want. You can put Ultimate Wolverine on a lunchbox or shirt with the Evolution logo, and it will still look correct. Wolverine even wore the same basic suit in Secret War, the event comic whose entire premise was "everybody gets new costumes," that's how badly they wanted to stick with it!
Animated Wolverine stuck to that costume until the end of the show (October 2003). Ultimate Wolverine wore it until the Ultimatum event (July 2009). Regular Wolverine switched clothes in Astonishing X-Men #1 (May 2004). So honestly, the idea of a "unified" look for the character never happened: the cartoon ended before Ultimate put it on. If you want to count the cover appearance, then there was a span of about 110 days where all three Wolverines were in the same suit before splitting off again.



Four Wolverines, actually: he also wore the suit in Activision's X-Men Legends and Marvel Ultimate Alliance games.