Nope. The "H.O." designation was first used in '82 to denote the slightly hotter version of the 5.0 that came in the Mustang. It was still a traditional short boss flat tappet block, just like all the others dating back to 1968. The Roller version did not come about until '85, and only in 4V, 5 speed applications. Cars ordered with AOD's got CFI, and used the flat tappet arangement, but it was still designated a "5.0 H.O" Roller blocks and cams did not become standard across the line until '86. H.O. engines also use the 351W firing order, as they used '73 351 Torino cams from '82-'85(CFI -only), then the firing order was carried over to the roller cams, mostly as an easy way to seperate the H.O and base engines.
As far as the 302 vs. 5.0, they are the same thing. Ford and most other manufactures were converting the traditional measuring system to Metric, so they started reffering to their engines in terms of "Litres" instead of "Cubic inches."
The first time Ford used the 5.0 badging was on the '77-'78 Mustang II.
Most people, not just old guy's, who have a little knowledge refer to the cars as "5.0. Mustangs", but will refer to the engine as a 302.
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