You should not interpret node names as meaning anything more than a point on the semiconductor roadmap. Nodes that share the same names across foundries will not have the same performance characteristics, but are usually roughly comparable (especially since Intel's new naming scheme).
I agree they're not necessarily related to any particular transistor dimension but are you sure it's entirely unrelated to any physical dimensions? If so, here is a question I have. 28nm, 22nm, 20nm, 14nm, 10nm, 7nm, 5nm, 3nm. What progression is that? Why skip 6nm and 4nm?
So 28 -> 20 is a "full node" decrease (ie: twice the transistors).
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We can see the full-node step from 14nm -> 10nm as well: 14 x 14 == ~200, 10x10 == 100. So its a full node step. The next full-node is 7 x 7 == ~50, which is half of 100. After 7 comes 5, because 25 is half of 50.
The next full node is sqrt(12.5) or 3.5, smack dab between 3 and 4, so not really easy to round.
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The steps in between are "half-node" decrements, where you didn't quite achieve a full 1/2 area reduction. An incremental technology that represents something in between the full node step progression.
x^2 is 1, 4, 9, 16, 25.
2^x is 1, 2, 4, 8, 16, 32