Carbonating, ,,,,,,,,
means that a reaction is actually taking place eg present tense, CD do this by having 2 seperate solutions ,  which travel down 2 seperate hoses and mix just befre they hit the carpet, they carbonate , at this point , the resulting reaction supposedly emulsifies the dirt more effectively than mainstream chemicals. The 2 solutions are hot, hence the Phrase "hot carbonating"
Carbonated  ,,,,,,,,,,,,,
Means that the solution  is full of carbon dioxide , eg fizzy pop,, any carpet cleaner  can easily and cheaply carbonate large amounts of any liquid ,,  you need a co2 cylinder, regulator and a suitable pressure vessel,  carbon dioxide is an acidic gas so high PH chemicals would be possibly neutralised.  If you were to heat a carbonated chemical , the co2 would be driven off. This is why CD  started the A/B  2 part solution and stopped using cold carbonated system in 1997.  It all works , IMO though it is over hyped and used as a selling /marketing point .