Well, up until the recent addition of some 400wattDE bulbs that were 'posing' as HQI bulbs (when they were really just probe start bulbs in a DE socket to try to cash-in on the DE=HQI perception), DE did mean HQI. With the small exception of those bulbs, every DE bulb is HQI... they are higher pressure, pulse start bulbs.
Where things get fuzzy is with SE bulbs. Some places like Marine Depot list all of their halides as HQI, when in fact, none of their SE bulbs are. There are some SE bulbs though, like the Radium, that are HQI in a Mogul form. This is what adds to the confusion.
And, to make things more confusing, 400wattSE bulbs come in both as well (since the HQI spec for 400watters on up was never migrated to the DE socket like 150s and 250s). It was only a couple years ago that those 400wattDE bulbs were thought up, and they werent even true HQI. There are only a few 400wattSE/HQI bulbs out there... the Ushio/BLV nepturion 10,000K, 14,000K, and 20,000K (non CWA models), the Aquaconnect 14,000K, and the Aqualine 10,000K, and they are all SE. Oh, there is a 400wattDE/HQI, but its a 5000K made by Radium.
There are a few more 250wattSE HQIs, like the Radium Cool Blue, but they are for the most part the exception to the rule. If its not made by a German company, chances are its not a HQI/SE. There are no US made SE HQIs that I have seen. Most everything made here is for here, and the US has been slow to accept anything but the cheap magnetic halides that buzz in high-bay pendants all over the country. When Home Depot started replacing their 400watt pendants with 54watt T5s, I was shocked.
But with the small exception of that failed attempt to introduce the 400wattDE bulbs, all 250watt and 150wattDE bulbs ARE in fact HQI rated.
Thats why I stick with DE... no confusion.