I was faced with the same confusion when I bought my phone. The box said it was a GT-i5800 and physically it was a GT-i5800. BUT, when I checked the firmware installed by entering *#1234# on the keypad I found the following:
PDA: I5801ZHJH1
PHONE: I5801ZHJH1
CSC: I5801ZHJH1
BUILD INFO : (I didn't note the exact details but it was 2.1 related)
According to samfirmware.com the letters 'ZH' are the country code for Hong Kong. So I think I got an unlocked unbranded phone installed with Asian firmware. I bought my phone from a UK based internet shop, so I can only assume their phone supplier was based in Hong Kong.
The first thing I did on realising I had an i5800 with i5801 firmware installed was to download the latest European stock version of 2.1 for the i5800, I5800XXJK1, from samfirmware.com and flash it to my phone using ODIN.
Having done that successfully I then upgraded to the latest European stock version of 2.2.
Interestingly a colleague of mine bought an unlocked unbranded i5801 whilst on holiday in Singapore. The Build No. was Froyo.ZHJPF and the baseband version i5801ZHJP3. He was experiencing problems with screen freezes etc. so I suggested he try connecting it to Samsung Kies to see whether he could update the firmware to 2.2. Not being very good with computers he got his wife to do it ! She had no problems with Kies and both updated their i5801's to the latest 2.2 version. I think they got the Asian firmware upgrade but the language is English and they are both happy, although my colleague thinks the battery is draining faster than before.
bjlabuk