Difference between samples and bounce samples when using BPT

When using the Branched Path Tracing, is there a difference between tweaking the bounce samples in Light Paths panel and the samples in the Sampling panel? It seems to me that it is the same but then why keeping both? Which one takes over the other one? Or maybe there is a difference?

The bounce parameters govern how far a ray will go before it is terminated (ie. number of times it bounces, the number of times it reflects, or the number of transmitting surfaces it goes through).

The sample parameters govern how many rays hit each pixel (on each pass) where a various shader component is present. So if you had a high number of glossy samples with all of the others at low values, you’ll find the reflections cleaning up far faster than every other part of the scene.

Ok, I got it! I still have some questions though. Here is a sketch of how I get it:

First of all, is the sampling settings only used for the first bounce, or also for all subsequent bounces? In other terms, is my sketch right, or is the bounce #2 limited to 1 sample whatever the settings because it is a secondary bounce and so it would be a waste?

Then, what happens with a material which is a mix of diffuse and glossy (like e.g. the principled)? Or a mix of glossy and transparent (like the diffraction)? Is the highest number used for samples?

And how is handled a different number of bounces for diffuse and glossy? If diffuse bounces is set to 1 and glossy is set to 2, will it bounce twice in my example of only once?

Also, transparency bounces are a bit confusing. Why such a minimum of bounces? What happens if the total number of bounces is higher than the minimum number of transparency bounces?

[edit] Another question: how is it that I get a reflection here while I have set 0 bounces? (glass BSDF on the sqare, emit on the cube and diffuse on the plane)

I’m not sure just how exactly BPT works, but areas covered only by indirect light also benefit from the concept of multiple samples per AA pass.