Does Donald Trump get both a presidential pension and salary?

According to the Former Presidents Act, no

a) Each former President shall be entitled for the remainder of his life to receive from the United States a monetary allowance at a rate per annum, payable monthly by the Secretary of the Treasury, which is equal to the annual rate of basic pay, as in effect from time to time, of the head of an executive department, as defined in section 101 of title 5, United States Code [section 101 of Title 5]. However, such allowance shall not be paid for any period during which such former President holds an appointive or elective office or position in or under the Federal Government or the government of the District of Columbia to which is attached a rate of pay other than a nominal rate.