The rear bumper is definitely different between short and long wheelbase. I believe the front is the same. Lower cladding is also different. LWB cars have a physically longer rear door than the SWB.

Since you have a 300SE, you have a SWB, and should have an easier time finding parts from grey imports. That back door was more or less shut down ~1985 or so, so Gen II Euros will be really tough to find without resorting to importing parts.

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Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]