He's off today. is the same as. He is off today. This means exactly what is being said. Nothing implied.- the person is not working today- He takes today off. This implies that the person that is "off today" has a habit of taking off this same day. (same day of the week, month) This person may always take off Mondays. He took off today. This implies that he usually is present for work/school, but for some reason decided to take today off.

I was a pilot and a flight instructor. When I "took off"", I left the ground with my student at the controls of our airplane.

Thanks, Jmat. You are right. I used the wrong tense.

By the way, I think you mean "He is taking off today" for the second one.