Thanks for providing the links.
It is very useful, yet another addition to my collection of info about WiFi, however it does not answer my question.
The "device" is selected by running "wpa_cli" , without any options, which by definition ( as stated in doc you have referenced ) finds "first" WiFi device.
I as a user have no choice to "select" which one.
In not so technical description - I am connecting RPi WiFi device to a router / modem WiFi device ( part of the modem/ router).
The "p2p" connection says in essence "direct connection - without intermediate router" so if should be "p2p" - one device is RPi(WiFi) and the other is a router (WiFi)
If I want t to connect Rpi (WiFi) to an internet then it would no longer be "direct" connection - RPi (WiFi) -> router/modem(WiFi)-> Internet service (wired connection) - hence "wlan0".
And same if the connection is RPi(WiFi) -> router (WiFi) -> local PC (wired -SSH).