Here's what i know about the HO engines compared to the non-HO:
HO engines originally came with the 351W camshaft, which had more lift and duration i believe (hence the 351 firing order), and later years used the 351 firing order, but with a roller camshaft (not sure when non-HO engines and 5.8's became roller cammed)
The HO came with valve reliefs as previously mentioned and forged aluminum pistons from '85 until '92 whereas non-HO were cast (as previously mentioned)
The HO engines came stock with Steel timing sprokets and double roller timing chains whereas the non-HO came with the silent type.
HO engines came with a reverse rotation water pump
HO engines came with better induction systems (all years) and better exhaust ('85+ for exhaust).
These are for the most part general statements but apply to nearly every year HO engine in most ways.
Hope this helped in some way.
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'84 Mustang 5.0 LX
My car