iPod touch Game Center Account Synced?

[App Downloader]

I signed in to Game Center on my iPod with a previously-created account made on my iPad, and all the achievements and games where all the same, but I remember I can't have the same account on 2 devices at the same time (got that from an old article), but it seems like they ARE synced.

Can anyone tell me whether or not Game Center accounts are synced or not?

 

[Menel]

It uses your AppleID, so yes, synced.
Achievements are synced.

 

[App Downloader]

Thanks!