If the drive came out of a 160GB iPod, then it would have been recognised as a 160GB drive by that iPod.
However, although you obtained the replacement drive from another 160GB Classic, the drive itself is - as you state, made by another manufacturer. That might might explain why there were two different versions of the operating system for the late versions of the Classic; 1.1.2. and 2.0.5. Perhaps the second iPod had the different version of the operating system, I don't know for certain.
The following article mentions this issue of the iPod only recognising 128GB of storage; http://www.alphr.com/audio/1001325/how-to-revive-your-old-ipod-classic-with-an-s sd . Although it refers to installing SSD (solid state drive) rather than another hard drive, perhaps it's the same issue.
In this article; Products – iFlash.xyz (where one can purchase Flash Memory kits for replacing the hard drive), it too mentions the 128GB limit. Although the site refers to a 7th generation Classic, I think it's usually known as a 6th generation 2nd revision Classic.
Note that both links are non-Apple sites. I'm not aware of any Apple documentation that addresses this.