The connector on the left has all the pins needed for fast-charging with USB-C according to the standard.
That said, the cable on the left has no pins for the cable configuration and USB2 data lines.
USB2 datalines are not used by chargers so that is not the problem.
I don't know if the charger on the right tries to do something smart but that might indeed be the reason why things go wrong.
Theoretically speaking, the cable configuration pins could signal the charger some information that is maybe interpreted incorrectly and thus providing the wrong voltage/current.
But it might just as well be a bad design where the voltage is too high.
But for determining that you need to special test equipment and willing to sacrifice another charger chip.
Nintendo implemented it's own fast charging protocol which is not compatible with that of the other/official standards.
Some power supply manufacturers just didn't get it right and the best example were those docks blowing up Switches.