Hua Lamphong is the name of both railway station and MRT Subway station. They are located close to each other. You can walk from the railway to the subway or vice versa.
Eastern Bus Terminal (Ekamai) is the bus terminal that you can take a bus to eastern Thailand such as Koh Chang, Koh Kood, Koh Samed, Pattaya, and so on. It is located on Sukhumvit Road and only a few minutes’ walk from Ekkamai BTS Station.
Hua Lamphong connects with MRT Subway, while Ekamai Bus Terminal connects with BTS Skytrain. If you want to commute to Eastern Bus Terminal from Hua LamPhong, here is my recommended option.
First option is to take MRT Subway from Hua Lamphong MRT Station to Sukhumvit MRT Station. Then, at Sukhumvit MRT Station, it connects to BTS Skytrain at Asok Station. Take the BTS Skytrain from Asok station to Ekkamai BTS Station. This option is suitable for people who are traveling with big luggage or traveling during peak hours (06.00-10.00, 17.00-21.00).
Another option is to take a taxi. The distance between these two places is about 10 kilometers and it should take around half an hour or more depending on the traffic. You can expect to pay 90 baht plus toll for a fare. This option is recommended if you come in group of 2 people or more because it is more comfortable and could be cheaper.
Hope this information helps