A sheet processing apparatus includes a sheet stacking portion arranged to receive sheets; a sheet discharging portion configured to discharge the sheets onto the sheet stacking portion; a first binding unit including a first receiving portion having a gap in a thickness direction of the sheets and being configured to receive the sheets discharged onto the sheet stacking portion by the sheet discharging portion, the first binding unit being arranged to perform a binding process, using a staple, on a sheet bundle including a plurality of the sheets received in the gap of the first receiving portion; a second binding unit including a second receiving portion having a gap in a thickness direction of the sheets, the gap being smaller than the gap of the first receiving portion, the second binding unit being arranged to perform a binding process, without using a staple, on a sheet bundle including a plurality of the sheets received in the gap of the second receiving portion; and a moving unit configured to move a sheet, discharged onto the sheet stacking portion, wherein, in the case that a sheet is moved into the first receiving portion, the second binding unit is arranged in a position in which the sheets moved into the first receiving portion by the moving unit do not enter the second receiving portion. The invention further provides an image forming apparatus.