Different 'connection types' between components
I'd say the best part of all this is a comment by @DKNguyen: "but in the end, is it useful?"

You can call those nodes any way you want... and in the end it will give you exactly zero useful information. Here is why:







simulate this circuit &ndash; Schematic created using CircuitLab

As you can see, I haven't changed anything at point B. It is still "3-way" or "extraordinary" or "node with branch" or whatever else you choose to call it.
But the whole function of the circuit changed. That is because individual points do not matter by themselves, only by the closed circuits they create en masse.