The regulator supplied is for the compressed air that is used by the plasma cutter .
Both of the regulators in your original post essentially do the same thing , drop the bottle pressure and allow you to control the flow rate .
The first one has the ball type flow gauge which is preferred as it is more reliable in the long run – those cheap needle gauges on the second gauge set can stick and jam up but the ball bearing in the tube is lifted by the actual flow of gas and has no moving parts to jam up . Both have bottle presure gauges that allow you to see when your bottle is just about empty , i have had these gauges fail as well but the regulator can still be used without it as long as the flow gauge is working .
It is worth the extra money to but a decent quality gauge set – it doesn't need to be top of the range but i would avoid buying a dirt cheap set . You will more than likely find both those gauge sets are made in china like just about everything else .
The bonus is you can use the same gauge on a mig welder as well .
Its ok to say a good welder working for a company can listen to the gas flow and know whether it is not set correctly when he or she doesn't have to buy the stuff ! When you are learning it makes life much easier to be to set the flow on a gauge rather than guessing it .
Take a look at these two youtube sites , you will learn something from them i'm sure :
Welding tips and tricks
Weld . Com .