If the front dashboard mounted defroster vent nozzles look like the reproduction ones below in your 1965 Coronet, then no, the rear window defogger vent nozzle and cover would not be the same part. I don't have any pictures of a rear window defogger unit for a 1965 Coronet to show you here, but maybe another member will and can share it with us.
Below are all of the part numbers that were used on the 1965 Dodge and Plymouth B-Body models rear window defogger units and in some cases on other 1965 A-Body, C-Body and Imperial models. I've also included the part numbers for the front dashboard mounted defroster vent nozzles at the bottom of this post that might help you in your parts search.
Part number: 2521 447
1965 Factory Parts Book section number: 1-47-1
Part description: defogger package, rear window
Number of this part used per car: 1
Application: 1965 Dodge Coronet models
Application: 1965 Plymouth Belvedere models
Part number: 2277 860
1965 Factory Parts Book section number: 1-47-4
Part description: louver, inlet, rear window defogger
Number of this part used per car: 1
Application: 1965 Dodge Coronet models
Application: 1965 Plymouth Belvedere models
Part number: 2277 861
1965 Factory Parts Book section number: 1-47-4
Part description: louver, outlet, rear window defogger
Number of this part used per car: 1
Application: 1965 Dodge Coronet models
Application: 1965 Plymouth Belvedere models
Part number: 2291 095
1965 Factory Parts Book section number: 1-47-7
Part description: switch, rear window defogger
Number of this part used per car: 1
Application: all 1965 A-Body models with rear window defogger option
Application: all 1965 B-Body models with rear window defogger option
Application: all 1965 C-Body models with rear window defogger option
Application: all 1965 Imperial models with rear window defogger option
Part number: 2496 788
1965 Factory Parts Book section number: 1-47-8
Part description: knob, switch, rear window defogger
Number of this part used per car: 1
Application: 1965 Dodge Coronet models only
Part number: 2497 250
1965 Factory Parts Book section number: 1-47-9
Part description: bezel, switch, rear window defogger
Number of this part used per car: 1
Application: 1965 Dodge Coronet only
Part number: 2076 423
1965 Factory Parts Book section number: 1-47-10
Part description: wiring, rear window defogger
Number of this part used per car: 1
Application: all 1965 A-Body models with rear window defogger option
Application: all 1965 B-Body models with rear window defogger option
Application: all 1965 C-Body models with rear window defogger option
Application: all 1965 Imperial models with rear window defogger option
Part number: 2277 849
1965 Factory Parts Book section number: 1-47-12
Part description: tube, rear window defogger
Number of this part used per car: 1
Application: 1965 Dodge Coronet models
Application: 1965 Plymouth Belvedere models
Part number: 2096 772
1965 Factory Parts Book section number: 1-47-13
Part description: motor and bracket, rear window defogger
Number of this part used per car: 1
Application: all A-Body models with rear window defogger option
Application: all B-Body models with rear window defogger option
Application: all C-Body models with rear window defogger option
Application: all Imperial models with rear window defogger option
Part number: 1239 241
1965 Factory Parts Book section number: 1-47-16
Part description: wheel, blower, rear window defogger
Number of this part used per car: 1
Application: all A-Body models with rear window defogger option
Application: all B-Body models with rear window defogger option
Application: all C-Body models with rear window defogger option
Application: all Imperial models with rear window defogger option
Part number: 2277 845
1965 Factory Parts Book section number: 1-47-17
Part description: housing, blower, rear window defogger
Number of this part used per car: 1
Application: 1965 Dodge Coronet models
Application: 1965 Plymouth Belvedere models
Part number: 2277 840
1965 Factory Parts Book section number: 1-47-19
Part description: clip, retaining, rear window defogger
Number of this part used per car: 3
Application: 1965 Dodge Coronet models
Application: 1965 Plymouth Belvedere models
Part number: 1842 965
1965 Factory Parts Book section number: 1-47-19
Part description: louvers, retaining, rear window defogger
Number of this part used per car: 6
Application: 1965 Dodge Coronet models
Application: 1965 Plymouth Belvedere models
And the part numbers for the 1965 Coronet front dashboard mounted defroster vent nozzles.
Part number: 2485 298 (passenger side)
1965 Factory Parts Book section number: 1-48-144
Part description: nozzle, defroster, right (passenger) side
Number of this part used per car: 1
Application: 1965 Dodge Coronet models
Application: 1965 Plymouth Belvedere models
Part number: 2485 299 (drivers side)
1965 Factory Parts Book section number: 1-48-144
Part description: nozzle, defroster, left (drivers) side
Number of this part used per car: 1
Application: 1965 Dodge Coronet models
Application: 1965 Plymouth Belvedere models
Richard