Well to further complicate this discussion - according to this website the "K" and "J" designation is about the shape of the edge of the wheel and not the "humps" in the rim...
J, JJ, K, JK, B, P AND D : TYRE BEAD PROFILES / RIM CONTOUR DESIGNATIONS.
No, my keyboard letters weren't stuck down when I typed this. The letter that typically sits between the rim width and diameter figures stamped on the wheel, and indicates the physical shape of the wheel where the tyre bead meets it. In the cross-section on the left you can see the area highlighted in red.
Like so many topics, the answer as to which letter represents which profile is a long and complicated one. Common wisdom has it that the letter represents the shape. ie. "J" means the bead profile is the shape of the letter "J". Not so, although "J" is the most common profile identifier. 4x4 vehicles often have "JJ" wheels. Jaguar vehicles (especially older ones) have "K" profile wheels. Some of the very old VW Beetles had "P" and "B" profile wheels.
Anyway the reason it is an "awkward topic to find definitive data on" is very apparent if you've ever looked at Standards Manual of the European Tyre and Rim Technical Organisation. It is extremely hard to follow! There are pages and pages (64 in total) on wheel contours and bead profiles alone, including dimensions for every type of wheel you can think of (and many you can't) with at least a dozen tabled dimensions for each. Casually looking through the manual is enough to send you to sleep. Looking at it with some concentration is enough to make your brain run out of your ears. To try to boil it all down for you, it seems that they divide up the rim into different sections and have various codes to describe the geometry of each area. For example, the "J" code makes up the "Rim Contour" and specifies rim contour dimensions in a single category of rims called "Code 10 to 26 on 5deg. Drop-Centre Rims". To give you some idea of just how complex / anal this process is, I've recreated one such diagram with Photoshop here to try to put you off the scent.
A reproduction of an ETRTO diagram describing rim contour design
From the tables present in this manual, the difference in dimensions between "J" and "B" rims is mainly due to the shape of the rim flange. This is the part in the diagram defined by the R radius and B and Pmin parameters. Hence my somewhat simpler description : tyre bead profiles.
Note that in my example, the difference between "J" and "B" rims is small but not negligible. This area of rim-to-tyre interface is very critical. Very small changes in a tyre's bead profile make large differences in mounting pressures and rim slip.
"A" and "D" contour designations come under the category of "Cycles, Motorcycles, and Scooters" but also show up in the "Industrial Vehicles and Lift Trucks" category. Naturally, the contours have completely different geometry for the same designation in two different categories.
The "S", "T", "V" and "W" contour designation codes fall into the "Commercial Vehicles, Flat Base Rims" category. The "E", "F", "G" and "H" codes fall into the "Commercial Vehicles, Semi-Drop Centre Rims" category. Are you beginning to see just how complex this all is?
I think the best thing for you, dear reader, is a general rule-of-thumb, and it is this : if your wheels are stamped 5J15 and you buy 5K15 tyres, rest assured they absolutely won't fit.
H, H2, FH, CH, EH AND EH2 : HUMP PROFILES.
More alphabet soup. So you might have just about understood the bit about bead profiles, but there's another design feature of wheel rims. The 'hump' is actually a bump put on the bead seat (for the bead) to prevent the tyre from sliding off the rim while the vehicle is moving. As with rim contours, there are several different designations of hump design and configuration, depending on the number and shape of the humps. For the inquisitive reader, here's a table of the hump designations, and a diagram similar to the one above which displays in nauseating detail just what a hump really is. The eagle-eyed amongst you (or those paying attention) will notice that this diagram is an enlarged view of the area around Pmin in the other ETRTO diagram above, because that's typically where the hump is.
Designation Bead Seat Contour Marking
Hump Hump Normal H
Double Hump Hump Hump H2
Flat Hump Flat Hump Normal FH
Double Flat Hump Flat Hump Flat Hump FH2
Combination Hump Flat Hump Hump CH
Extended Hump Extended Hump Extended Hump EH2
Extended Hump 2+ Extended Hump 2+ Extended Hump 2+ EH2 +
etrto hump contours
If you're obsessive-compulsive and absolutely must know everything there is to know about bead profiles, humps and rim flanges, you can check out the ETRTO (European Tyre and Rim Technical Organisation website from where you can purchase their manuals and documents. Go nuts. Meanwhile, the rest of us will move on to the next topic.