GFWL achievements same as 360?

This might seem like a really silly question, but when I'm looking at achievements on my 360 or the xbox console companion, this version of the game comes up like its a 360 game. So if I started the 360 version, would I be able to continue from there or do I still need to do the PC version with the busted GFWL?

The 360 version and the GFWL version have the same achievements but are two seperate lists.

If you start the 360 version you will be able to complete the 360 version without having to start the GFWL version.

The only games with that are the ones without "(PC)" in the name in the GFWL games I guess?
These 5:
BlazBlue: Calamity Trigger Achievements
Game Room Achievements
Lost Planet: Extreme Condition Colonies Edition Achievements
Shadowrun Achievements
Universe at War: Earth Assault Achievements