Deduction, abatement, rebate, discount are comparable when they mean an amount subtracted from a gross sum.
Deduction is interchangeable with any of the others but not without some loss in precision.
An abatement is a deduction from a levied tax or impost.
A rebate is an amount deducted and returned after payment either in adjustment of an overcharge or to gain a competitive advantage.
A discount is a deduction from an amount owed or a price asked in consideration of a cash or prompt payment. It also may denote an advance deduction of the amount of interest payable on a loan or note from the time the loan is made or the note purchased until the due date.