***** NOT A TEACHER / ONLY MY OPINION
I believe that there is a huge difference.
(1) Can I take a message?
Someone calls your home in order to speak with your sister.
She is not at home.
You tell the caller: Can I take a message (from you and give it to
her when she returns)?
(2) Can I leave a message?
You call your girlfriend's home.
Her mother says that your girlfriend is not there.
You ask her mother: Can I leave a message (and you give it to her
when she returns)?
P. S. Of course, in the first example you could also ask:
Do you want to leave a message (for my sister, to whom I will deliver it
when she returns home)?
Student or Learner