Sorry, I’ve no idea what the difference is between the road and mtb versions of Chris King bottom brackets??!!

Are they interchangeable??

No as are road/mtb specific. They have it stamped on the b/b shell.

What makes them ‘specific’ then??

Surely an english threaded road BB can be used in a mountain bike (Shimano manage it).

From CK web site – though I thought it was the number of threads on the cup and not sure what dimension they mean by “width”
Road and Mountain cups are almost always specific to discipline-specified crank systems. While the bearings are identical for both versions, the overall width of the cups is what designates use for a certain system. Cups are designated with two identifying marks per cup along with installation direction and torque values. There are, however, instances of compatibility where a “MTN” cup will be used for a “ROAD” crank. Please contact us or ask your favorite mechanic for advice.