3nm and 5nm are just marketing names it does not represent any geometry of the transistor. Probably the best analogy is 3nm would be the average length of the side of a pixel. One draws a transistor, or anything else, from many pixels.

The exact details are under NDA but to get a 'very' approximate idea of the scale of things one can look at the 5nm Wikipedia page.

They list the metal pitch as 30nm in TSMC's N5 node so in general two pieces of metal cannot be within 6 'pixels' of one another. One gets a rough guess on the distance between transistors by looking at the gate pitch (roughly 10 pixels in this case) but that measurement comes with a lot of caveats too.

Keep in mind this is when you're going out of your way to make something tiny but there are many good electrical engineering reasons to make the transistors larger still, and quite a lot of them are.

https://en.wikipedia.org/wiki/5_nm_process

Wikichip is also great. https://en.wikichip.org/wiki/5_nm_lithography_process

> That's interesting - are they just entirely making that up then? What's the 3nm supposed to represent?

A progression over 5nm. That is all.