A blackboard is:-
a sheet of smooth, hard material, especially dark slate, used in
schools, lecture rooms, etc., for writing or drawing on with chalk.
whereas a chalkboard is:-
A smooth hard panel, usually green or black, for writing on with
chalk; a blackboard.
A greenboard is:-
a green chalkboard or blackboard.
Note that the second reference also defines chalkboard as:-
(Social Science / Education) a US and Canadian word for blackboard
which leads us to the nub of the matter. I won't pussyfoot around the point here; greenboard and chalkboard were invented to avoid including the word black, which offends the political sensibilities of some people.