Hua Lamphong is the name of both MRT subway station and railway station. The railway station is the main railway station in Bangkok and it connects with MRT subway station. You can take a train at Hua Lamphong to Northern Thailand, northeastern thailand, Southern Thailand, and Eastern Thailand.
BTS or skytrain is a rapid transport system in Bangkok. Nowadays it is a major transportation mode for people living and working in Bangkok. If you are researching information about Bangkok, I am sure that you know it!
However, Hua Lamphong does not connect with the BTS. If you want to go to BTS Station from Hua LamPhong, here are my recommended options.
1. The nearest bts to hua lamphong is Sala Daeng Station which connects with MRT at Silom Station. You just take the MRT from Hua LamPhong and get off at Silom Station.
The name of BTS and MRT Stations might make you confused. They are on the same place, but difference name (BTS Sala Daeng = MRT Silom).
2. Another option is to take the MRT from Hua LamPhong and get off at Sukhumvit Station. The station connects with BTS at Asok Station (BTS Asok = MRT Sukhumvit). You might choose this option, if you want to go somewhere on Shkhumvit Road such as Thong Lo or Ekamai.