Yes, same set of listed shares. I'm not 100% educated on the...

Yes, same set of listed shares. I'm not 100% educated on the mechanisms of how the shares get transferred to be traded on the OTC market, but the OTC market will unlikely do any "driving" of the share price on the ASX. The main effect of being listed on the OTC is to open up and cater to demand that aren't able to transact on the ASX. There will be market arbitragers that will take advantage of any price differences between the ASX and OTC so if OTC overshoots to the up side, they can increase supply on the OTC by buying it cheaper on the ASX which would bring the price back down on the OTC (and vice versa). You would need really significant volume on the OTC to be a major price driver on the main exchange, which generally doesn't happen as those with deep pockets and would buy in large volume would do it on the main exchange. I believe trading on the OTC markets has higher brokerage fees too.