No hyphen; adjective only. Avoid in print the noun “postdoc,” informal academic jargon for a postdoctoral position or research or funding, or for someone engaged in postdoctoral work.

Is postdoc capitalized?

Use lower case for “freshman,” “sophomore,” “junior,” “senior,” “graduate student” or “postdoctoral fellow.” Do capitalize these words if they are part of a designation for an entire class or a formal title.

What is the difference between PhD and postdoctoral?

The first and foremost difference between the two is that a PhD is "awarded" after defending a thesis (plus additional duties depending on the department). On the other hand, a PostDoc is a temporary working position that is assigned by some institution, whose completion does not require any defence.