I realize the push for difference from Stewart is referring to the character but the show itself is actually legally required to be different from the prime timeline we all know and love due to the split Star Trek copyright. I mean it mainly means different visual styles but also a different tone, and implied different continuity.

All the current Star Trek shows under Kurtzman's reign fall under the Paramount/Viacom copyright which does not include any of the Trek tv shows (which fall under the CBS copyright), so they are required to make everything visually distinct, which explains the changes to everything in the Kelvin films and the look of ST: Disco, despite how they insisted it takes place in the Prime Timeline, and yet looking so different with inconsistent technology for the established time period. Legally these new shows cannot take place in the same universe unless the copyrights are somehow merged again. For whatever reason, CBS is having these shows made under the Paramount copyright instead of their own.

I read somewhere that the design of the USS Enterprise as it appeared in Disco was required to be at least 25% different than it was from TOS. Should the Picard show ever show the ol' Enterprise D from TNG, it will most certainly look fairly different from the show. However interestingly enough, the less popular Enterprise E could appear exactly the same because it falls under the Paramount copyright.