They were:

From the Ming-shih, ch. 326 (concluded 1724 C.E.), for 1368-1643 C.E.:

[F]u-lin [Byzantium] is the same as [Da Quin]Ta-ts'in [Roman Syria] of the Han period.

They were picky about this since early Ming Dynasty scholars did cast some doubts about if both were the same or not. But this was the result of isolation from the tributary embassies of the Byzantine Empire because firstly of the crusades and then of the Mongol conquests and eventual Yuan Dynasty in China, where foreign relations were held largely exclusively by ethnic Mongols. When ethnic Chinese regained the control of their foreign relations at the Ming Dynasty they had to make a lot of catch-up paperwork, and it wasn't until later in the dynasty than the mess up did resolve.

With that said they were aware as early as the Tang Dynasty that the nature of how Fu-lin behaved was clearly different despite being technically the same state.

Source: http://sourcebooks.fordham.edu/halsall/eastasia/romchin1.asp