I'm wondering if there's a distinct, official version of x86 android that's different from the ones made through the Android-x86 Open Source Project (http://www.android-x86.org/). I'm asking since that project was started some time ago and predates versions of android that officially support x86. Also, I'm now seeing phones that use intel atoms running android like the Asus ZenFone 2, so do those phones use the same iso images provided by android-x86.org? If not, what's different about the x86 android os those phones are running compared to what you get from android-x86.org?
First of all, what do you mean by official? You mean released by Google?
And no, the firmware on Asus's x86 Android devices are certainly not the same builds released by Android x86.
All Android releases are based in one way or the other on the code released by the Android Open Source Project, a Google initiative.
Anyone could take that source code, customize it, and make their own Android release.
Android x86 also uses this source code, but they have put in heavy work compiling it for x86 and constructing a kernel that's compatible with normal PCs. Android x86 is explicitly unofficial, and is not affiliated with Google.
Remix OS is a derivative of Android x86. While it is built by former Google employees, it is also unofficial and not backed (nor opposed) by Google.
Asus distributes their own Android builds for their x86 devices, but it's not Android x86 as in the PC project I referred to above. Asus Intel phones are (unfortunately) not normal PCs where you can just install any OS you want. (Although that would be super cool if they were.) They are just like any other Android phone (except they have x86 processors), in the sense that they require a ROM that is specifically tailored to their hardware. (Unfortunately, Android devices don't follow a convention the way PCs do.) Asus develops such tailored ROMs, in the form of their stock firmware.
Is this firmware an official x86 version of Android? It depends what you mean by official. It is officially developed by a large corportation, Asus. It ships with official Google software, apparently approved by Google. I don't know if you could call that official. Depends on your viewpoint. However, these ROMs are strictly for the device they were built for. It's not like PCs where you can just swap OS installers around and use any OS on almost any device. (Again, I really wish it was, but what I personally wish for is not really relevant here, so forgive my blabbering.)
I'm not aware of any Google product (like a Nexus) with Android and an x86 processor.
Interestingly, Google is bringing official Android compatability to Chrome OS, a somewhat popular PC operating system that runs on both ARM and x86 and is also (mostly) released under the open source Chromium OS project. Both Android and Chrome OS run on the Linux kernel. So what differentiates them? The userland and other components (which is a huge difference.) It looks like, however, that Google are porting all or most of the Android userland to Chrome OS. So would Chrome OS then qualify as an "Android release"? Well, it depends on how you define an Android release. It runs on a similar Linux kernel and has most of the same userland integrated. If you're willing to stretch yourself, I guess you could call that an "official Google Android release for x86." Of course, it also has the Chrome OS userland. But Maru OS similarly has the whole GNU userland, and Maru OS is still and Android release.
Confusing? Yeah, I guess it can be. Thankfully there are some pretty smart engineers working on all of this. After all, Android is one of the most popular and user friendly operating systems on the planet.