Cinema EQ is the non-THX brand of Re-EQ. It's purpose is to lower treble levels at home for cinema soundtracks. High frequency energy dissipates more quickly in a very large room than other frequencies so cinema soundtracks are typically mixed with boosted treble to compensate, but at home, it's too much treble in smaller rooms so it can sound a bit harsh. Re-EQ/Cinema EQ reduces the treble to sound correct in the home environment.
The problem is since 1999 or so starting with The Phantom Menace and including The Matrix, which I have the actual AptX cinema DTS mix for to compare, Hollywood started making "home mixes" that already correct this (and often reduce dynamic range in favor of louder dialog as that's their #1 complaint from people (who probably have hearing problems/damage).
A few studios didn't generally follow this practice for many years (Paramount comes to mind, especially the Raiders of the Lost Ark THX Blu-ray which I could play at home at reference levels precisely because it is the cinema soundtrack! Home soundtrack mixes reduce dynamic range (louder on everything just like the CD music loudness wars) making reference levels unbearable in the process (why you usually can't stand movies that loud at home).
Unfortunately, there is no flag or anything to mark which soundtracks are cinema mixes and which are home mixes, but mixes after 2001 (including newer "remastered" or Atmos mixes) are usually home mixes. Some studios may have altered dynamic range or levels before that, but probably didn't apply EQ.
How big are some of the differences? The Matrix in Cinema DTS has about 7dB more dynamic range (i.e. Matched for dialog level, the big sound effects like explosions are 7dB louder on the Cinema DTS mix (that's 70% louder sounding with same level dialog). Suffice to say, the Atmos mix sounds pretty wimpy by comparison and yet people have no idea and think the Atmos mix is awesome. I use the DTS mix with Neural X instead. It's crazy good.
Turbine released "Twister" in a dual Auro-3D / Atmos release with completely separate teams doing each mix. Both are among the best immersive mixes I've heard. They both have stunning surround sound and overhead effects (tornadoes ripping the roof off!)
But the Atmos mix has dynamic range tweaked 8dB down for louder dialog (home mix) while the Auro-3D team apparently wanted to preserve the theatrical levels with new immersive mixing. With matched dialog levels, it's a full 80% louder (8dB) on sound effects. The sound effects are downright terrifying at those levels (assuming your system can play that loud). It might be the most impressive soundtrack I've ever heard in that respect. I had to turn on the room lights to make sure the roof was still there!