I have an SE 2004 but it has almost all the options aside from 3rd row and rear air suspension. It does have dual sunroofs, heated seats and windshield, rear parking sensors, fog lamps.
What I noticed only recently is the passenger seat also having the arrow on the seat control pointing "up/down" on the backrest adjuster like on my driver seat. this "up down" movement of the backrest lever is for the lumbar. my SE does not have the arrows and does not adjust a lumbar feature. Aside from that, I don't know of any "inherent" HSE vs SE features because as I said, I think back then you could pretty much order all the options onto an SE but for some reason this person didn't just start with HSE. Maybe HSE came standard with rear air bags and not everyone wanted that added complexity.