I’ve seen in some places that Eurotrance is also known as HandsUp, yet they don’t explain why. The first examples they put are from the late 90s, and they’re not Hands Up since the name HandsUp
came from Manian in 2003 and he still uses it. It also makes no sense to call EuroTrance a HandsUp song when they don’t really have many “Trance” parts, so I would say the name Eurotrance
was somehow mixed up with Hands Up.
I think it’s the same problem as EuroHouse since they’ve been mixed up with other music styles, so this is my conclusion:
I don’t know when, some unknown people started to use the words EuroTrance and EuroHouse to describe EuroDance but in a more “trancy” way (EuroTrance) and the same but with some house characteristics (EuroHouse). Since they’re a way that not many people used to distinguish different EuroDance styles, there isn’t any really known artist who used them correctly, so people have left them behind and somehow someone must had mixed them up.
*Example of website saying what I think it's wrong.