How does the ability of the creature in "The Man Trap" work? Is it a mind trick, as it's indicated during the very first encounter with the away team (since each crew member seems to see a different woman) or does it actually assume the shape of a certain being? If the former case were true, this ability would stand in stark contradiction to the way it got onto the Enterprise, since it must hence be assumed that the crew on board didn't realize that they beamed up not crewman Green but a monstrosity. If the latter case were true, this ability would be in stark contradiction to the first encounter, since the creature must shape-shift continually without anybody nearby noticing it.
Obviously that being was able to transmit abstract perception images.
At the first encounter, it had no concrete idea about what would be the most effective (defensive) appearance in the current situation, so it might have suggerated to be a "sexual attractive mate", so a woman might have seen a cute guy.
While going onboard the ship, it knew it had to be a certain crew member in order to stay covered, and thus chose a concrete suggeration.
I think that the creature can actually shape-shift but also has telepathic abilities which allow it to appear as multiple women who have the same general body structure, so that if you touch her you wouldn't notice a difference between the three (as opposed to if you touched the creature in its true form). Her telepathic ability is further shown when she is able to speak Swahili to Uhura. Also when her powers are being described in the episode they describe her having the ability to assume any form, implying actual transformation rather than illusion as when they were describing the powers of the Talosians, but obviously she also possesses the ability of minor differences in how she looks depending on who is observing her but keeps the same general body structure.