difference between accessibility checker and pdf/ua checker

Disagree with some of that explanation.

The PDF Accessibility Checker (Tools/Accessibility/Full Check) since Acrobat CC:2018 has been based on PDF/UA-1, not on WCAG 1 and 2 as in previous versions of Acrobat. You can see this in the specific items it's checking: List structure, for example, is different in PDF than in HTML/WCAG. So are links, page/document content structure, and several other items.

So it is a valid checker for PDF/UA-1 compliance. But I said a "valid" checker, not a complete checker.

The Preflight checker for PDF/UA-1 is a mash-up of tests. Note that it is found in a tool panel labeled "Print Production," and I know of no standard that requires print-quality PDFs be digitally accessible for assistive technologies.

So although I agree that the Preflight checker's test is more "granular," I really call it "insanely granular with stuff that has no bearing on accessibility and is a waste of everyone's time."

Like checking the color space: is it RGB? CMYK? LAB? Does this really matter to someone who is blind or anyone else with a disability using assistive technologies?  How about bitmapped/raster images vs. vectors? Resolution of graphics? Trapping? Bleeds, crop marks, trim boxes, printers marks...all of these are print-related concerns, not for accessibility.

So some of those "added requirements" aren't requirements at all. They're someone's opinion, or a suggested "best practice" at best.

Lastly, the Matterhorn Protocol is nothing more than a working test of theories and examples by members of the PDF Association. It is not a law, standard, or anything else that's required to be followed. Just a draft or test of what makes an electronic document accessible. Or COULD make a document accessible--some ideas there don't last long. Since most members of the ISO committee that writes the PDF/UA standard are also members of the PDF Association and work on the Matterhorn Protocol, you are correct to assume that the theories tested in Matterhorn do make their way into the ISO PDF/UA standard.

But only us geeks and geekettes who work on the standards should be concerned about Matterhorn.

If your job is to make accessible documents, then you should know, master, and understand PDF/UA and possibly some WCAG that's appropriate. But not Matterhorn because it's not a standard authorized by an authorizing entity (like the ISO), and it's certainly not mandated by any law anywhere.

Bottom line: neither tool does the job we need it to do.

Each misses critical accessibility points. And one tool has crapahola in it than is not needed for the standard; this confuses users and obfuscates the real critical issues we should be working on.

Suggested Solution: (and feature request for you to submit to Adobe's Acrobat team, Chad!):

1. Merge the Print/Preflight checker into the Accessibility panel's checker, and migrate only the checkers that make sense for accessibility and PDF/UA-1 (and forthcoming PDF/UA-2). Nix the resolution, color space, etc. stuff. (And seriously, nothing for accessibility should be under tools labeled "Print.")
2. Beef up the Accessibility checker so that it assesses more items than its current version does (which will mostly happen when A is done, but there's more to check).
3. The checker must adhere to the standard: that is, don't leave anything out. But also don't add in anything that's not in the standard. Add-ins are NOT what has been agreed to by the ISO Committee; they are merely someone's opinion or a government agency's idea of what would be nice, or a software company's suggestion because they've developed a tool to fix the problem that they identify is a problem.
4. And don't jump the standard! The PDF/UA-2 standard isn't even completed yet, let alone submitted to the ISO and approved for publication by ISO. So don't put in half-baked non-standard stuff into a checker. Standards first, then the checkers, authoring software, assistive technologies, etc. based on the standards. Standards first.

Apologies for the rant. Can you tell that I'm in near-daily meetings about this stuff?   Gotta getta life.

The difference is that each one checks to a different standard. Where the Acrobat Accessibility Checker loosely checks to the WCAG 2.0 standard, PDF/UA or "Universal Accessibility" is based on the Matterhorn Protocol and checks to a more granular level. You'll almost always find more errors checking for PDF/UA due to the added requirements.