Just to answer OP's question and to elaborate a bit more:
No, it's not the same cigar. The one you are referring to is "Gurkha His Majesty's Reserve." It's infused with Remy Martin Louis XIII Grande Champagne Cognac and sells between $300-$400 a pop.
Apparently, this is not the only Gurkha cigars infused with Louis XIII Cognac. A quick search shows Gurkha The Royal Reserve, around $25/pop, Gurkha Grand Reserve, around $10.50/pop.
A notch below is Gurkha Private Reserve, infused with XO Champagne cognac. I am sure you can find a few more different Gurkha cigars infused with XO Cognac.
Then there is the one you listed, Cognac infused. Not XO Cognac, just Cognac. This is probably the one Bill Clinton used.
Other than the Gurkha His Majesty's Reserve, most of the rest are usally 3 for $21 around here. Prices are up lately because of MAP and the lack of selection available.