The original Mac was just called the Apple Macintosh, which had 128KB of RAM. Then, 8 months later, when the 512K came out, the original model was re-designated the 128K, so users knew which model they had. So, the back case of the original Mac just says Macintosh, and the newer 128Ks say Macintosh 128K.

Using the serial number, there are a few websites out there that help decode exactly what your model was built as. My upgraded Mac Plus has a serial number ending in M0001WP, which tells me it was originally a 512K before the upgrade. By checking this, you should know where it was made, the year, and the model when it left the factory.