Branding may have differed across different markets; obviously you're not in the UK where I am, so you may have had a model called HGT in your country.
In the UK it went a bit like this:
2.4 cars started off being called the Abarth - both 3 door and five door.
Then, I think around 2003ish, the range got a revision.
The 3 door model then because known as the Abarth and the five door model got called the Prestigio. All with 2.4 engine.
You also have in the mix the Schumacher limited edition models too.
The UK market never got a HGT spec for Stilo. Some other Fiat models in UK do carry the HGT spec though.