Why is an aircon with 34000 BTU cooling capacity uses less current than a 14000 BTU unit?

The current rating has to refer to the peak demand, most likely the startup current. The 14000 BTU unit might start the fan and compressor at the same time while the 34000 BTU unit manages the startup current to something reasonable, like a soft-start. When it comes to the average power consumption the 34000 BTU unit has to consume more. Maybe the average current of the 14000 BTU is like 5A and the 34000 BTU is 9A (those are guesses).

For the wiring you really need to look at the installation instructions. I will say that it looks like the RZR50LVVM would be a single phase in a country such as the UK where you get 230V on one phase. If you used the same thing in the USA, they use a split-phase, where a regular house only has 1 phase coming in but it's split and has opposing voltage, so 1 to neutral is 110V but 1 to the other is 220V and some people will call this 2 phases, so in the USA you would have to use 2 of those because for 60Hz (USA) it says 220-230V, but for 50Hz (ex. UK) it says 220-240V so that is like their regular mains voltage from 1 phase to neutral.