Yes, both institutional and retail investors pay the same price in OnMarket capital raisings.
The price of an OnMarket offer is determined by the lead manager and the company issuing the securities. In a fixed price offer, all investors apply for a number of shares at a price that is set for the duration of the offer. All investors are then allocated at that price.
In a variable price offer, OnMarket (and other) investors are invited to apply for securities at the maximum price they are willing to pay. The company and lead manager will then make a decision as to the final price that they wish to close the offer at, and all investors whose applications were at or above that final price will be allocated at that final price.