In what ways might the professed motives of western explorers and colonists have differed from their real motives? would they necessarily have been aware of the discrepancy?

There is a commonly accepted understanding that explorers and colonists had religious motives to explore the world and teach the real belief, Christianism. But, as the matter of fact, Columbus was looking a route to the east (China and India) by going west because the Muslims had cut off the traditional route through land between Europe and Asia and were asking for high taxes in order to let the merchants pass through that way. To find a new route of commerce not controlled by Muslims is what they were looking for.

All the men that sailed with them were from the lowest of the society, often trying to avoid jail time for some crimes they have committed. Some of them were adventurers. They were not la creme de la creme of society, nobility and trustworthy people. They set to the New World because they were no one and there they could be powerful and rich. When the different monarchies realized how valuable the New World was, they send trustworthy people to build an empire under the control of the Spanish, Portuguese and English crowns.

Some religious people sailed to the New World to spread Christianism. But this was also an instrument of control of the population there.

To say that they were spreading th true religion and saving the souls of the millon in the Nw World was a way to legitimize the construction of the Empires. People in charge knew what they were doing, and people following orders were just people following orders, although they had room to do pretty much what they wanted far away form the bosses in the metropolis.