AFAIK
I need to probably explain what i mean by jin a bit better. Jin is the force/strength/power created by a manipulation of energy. The character for Jin is an underground river and "li" strength combined - i.e. the strength which comes from the underground river. Underground river - internal energy.
I don't want to go into the shitstorm which would be how you manipulate qi to provide jin, its different for everyone, personally I think body movement plays a big part in it but there's other factors going on which I couldn't adequately describe in text as it is really something which is experiential.
Anyway, what the internal energy does (however you may do it) determines the jin. If the energy is sprialing you get zuan jin, if its rising or falling you get pi jin, if its expanding or contracting its beng jin.
The main energy (not "the single energy") being used in pao quan is expansive so it is beng jin which will be applied.
Beng jin is expanding or contracting of energy. In general beng quan begins slow and gets faster - i.e. it accelerates gradually (or fast to slow deccelarates - you get this in half step beng obviously because the forward momentum is stopped by the shorter step); though gradually is usually still pretty fast for most people.
Pao I think is more related to the movement, structure and the quality of "explosivity" because it doesn't have a "jin" of its own its purely a method in itself which uses other energies. Anyway pao quan goes from 0 to 60 in a flash - the expansion is explosive. Not just faster than beng quan but much faster. Pao has bits of zuan jin and pi jin and other things in there too, its not very clear cut compared to the other movements but I'd argue that its mainly using beng jin and using it over a much shorter time than beng quan or heng quan would.
But its not "just" the timeframe because Pao has a lot of things going on whereas beng quan is a more simple movement. Just doing a beng quan faster than normal wouldn't give you a pao quan but it would be damn near.
We're getting right into it here now. Beng is related to the phase of wood. Wood can expand and contract and store and release energy. If you think of roots growing through rocks they eventually break the rocks but its a gradual process. Pao is related to fire (or the essence of fire) and to explosion, you put gunpowder in a crack in a rock and it blows it apart straight away. The same kind of energy is used - an expanding pressure but the timeframe is different and as Teazer pointed out the application is different.
Now to add another level of complexity. If you perform a beng quan movement but your internal energy is spiralling you get beng quan with zuan jin dominant - this is very strange indeed you expect a straight penetrating hit and you get your insides twisted instead. Can't say I can do this but I've felt it once or twice.
One penetrates and goes thru the target thru a single point, like an arrow. The other explodes in all directions and creates a shock on impact, like a cannon.
IMO the reaction is different but the power which creates the reaction is the same, the method in which the power is applied creates the difference in reaction. I agree that beng quan can focus the force more than pao quan, and i'd argue that this is because there is also some pi (rising or falling) and zuan (spiralling) in there too. When I do pao I still try to make it penetrate like an arrow, just like a really fast arrow with a bomb strapped to the tip.
