Noone needs to know the difference between AT and enhanced AT any more. They usually call the latter regular / full size / ANSI / ISO.
I disagree that F type is clearer. If anything, most people would think of the XT layout then. I have a Model F with 122 keys on the way!
The only thing AT about a minitouch is the connector and signalling, which has nothing to do with the layout. WTF are full minis? Do you mean that which everyone else on the planet calls either tenkeyless or space saver (sic)?
I'm sure people would've known what you meant if you'd described this board as: 'AT layout with blue Alps'.
I would quite like an F-type...
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The XT F type is exactly the same as the AT F type except for the enter key and a few other keys, 1 extra key, and a separated numpad, so they're both f types. The layout is almost exactly the same. That one that was linked to with an extended middle set of keys is an extended f type in my mind. It's the best way to describe it in a title, because there are other formats for AT 84 key keyboards these days.
A full mini is a fully compact board with no extra set of keys other than the main keyset on the right, like the mck-84, or minitouch. A tenkeyless or spacesaver usually just has the numpad or middle arrow key set cut off, which is not a full mini.
Boards like the hhkb I would consider a super compact, or just hhkb type.
Think of it like ship types. It's the first ship of that configuration that the class is named for. It should be the same with keyboards or at least best known. That's the clearest way to do it when describing the layout to other people because it invokes an image.
In order of progression.
The M type is the standard.
The side function keyed board is an F type.
A tenkeyless is like the Filco/Majestouch Tenkeyless.
The Mini is the MINItouch type.
The super mini is the hhkb type.
Ultraminis would be anything under that with either shrunken keys like thumb boards, or one handed worn/ non standard key layouts, for instance a chordite might also fall into this category, although that might even be another one.
All keyboards that work with modern machines are AT type, so the minitouch and ortek boards are also 84 key AT boards. Neither of those terms are descriptive of the layout. AT is only a description of the technology and interface the board uses(bidirectional as opposed to unidirectional in xt) and means "Advanced Technology", nothing else.
The terms you're trying to impose on them only had significance when there there only those two types of AT boards in existence. These days there are a lot of other formats, and F type is the easiest way to describe the format, unless you can come up with a better one, which imo you really haven't.