A helpmate with identical final positions in set play and actual play with exchanged squares (or existence) of two pieces of the same kind and color.
See also: Place exchange in the final positions.
Larsson, Bror
Schachmatt, Stockholms Problemschackklub TT, 1949
4th Prize
1...Se3
2.cxb1=R
Sc2#
1.cxd1=R
Sa3
2.Rb1
Sc2#
Fuhlendorf, Gerhard
Deutsche Märchenschachzeitung, 1931
1st Prize
1...Rxd4
2.Kc5
Rh5+
3.Kxd4
Rd5#
1.Kc5
Rxe3
2.dxe3
Rh5+
3.Kd4
Rd5#
Larsson, Bror
Springaren, 1953
1st Prize
1...Sg4
2.Rhh5
Sf2
3.Rhd5
Sf3#
1.Rd5
Sh3
2.Rc1
Sf2
3.Rcc5
Sf3#
Moder, Janez
Partizan TT, 1958
1st HM
1...Rb6
2.Bxg8
Rh6#
1.Bxb3
Rg6
2.Bg8
Rh6#
Shapiro, Misha
harmonie, 2010
1st Prize
1... ... 2.a2
exd7
3.axb1=B
d8=S
4.Bh7
Sxf7#
1...Sxa3
2.Bxe6
Sb5
3.Bf5
Sd6
4.Bh7
Sxf7#