Impostor refers to a kind of person, while imposture refers to the actions that make a person an impostor.
An impostor is a person pretending to be someone else, or a different kind of person than they really are—or as we say, “posing”:
The impostor was kicked out of the meeting when he failed to show the correct identification.
You may have heard the popular phrase and idea impostor syndrome, which is when a person feels like they are being an impostor in some role, such as a job, due to self-doubt about their abilities:
Impostor syndrome is common among professors who expect themselves to know everything.
Impostor does not only describe people in a role or job. It can also refer to a person who is pretending to be a specific different person:
There is a mental illness where people believe their loved ones are impostors.
Imposture is the state, condition, or act of being an impostor:
The fake professor’s imposture was not very convincing since he was unable to answer any questions about his research.