Jeff - There are two factors involved in this - the "arms" as Ford calls them, meaning the mounts, and the bumpers themselves. Our page at Documentation/Exterior/Bumpers has a Rear Bumpers tab. And in that there's a Part Numbers tab where you'll find the PN's for the arms and the bumpers themselves.
The arms appear to be the same from 1980 through 84, and then again from 85 through 89, which is what "85/" means - 85 to end of catalog.
But in the bumper section there's the entry below and that bumper fits from 1980 through at least 89. So whatever change was made between 84 and 85 was apparently for the frame as the same bumper fits both years.
So yes, I believe the bumpers will interchange.
Gary, AKA "Gary fellow":
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Dad's: '81 F150 Ranger XLT 4x4: Down for restomod: Full-roller "stroked 351M" w/Trick Flow heads & intake, EEC-V SEFI/E4OD/3.50 gears w/Kevlar clutches
Blue: 2015 F150 Platinum 4x4 SuperCrew wearing Blue Jeans & sporting a 3.5L EB & Max Tow
Big Blue: 1985 F250HD 4x4: 460/ZF5/3.55's, D60 w/Ox locker & 10.25 Sterling/Trutrac, Blue Top & Borgeson, & EEC-V MAF/SEFI