Are system specification and functional specification the same?

No. Often, system specifications differ from functional specifications on various degrees.
They may be performance-based differences, implementation differences, engineering and design differences, or logical differences.

For example, many hard drives are specified as '500GB' but may be functionally only 488 GB, as an example.

Another example is that a system may have functional and specifically 4096 MB (4 GB) of RAM. But system differences [such as 32-bit memory wall limitations and shared video) can reduce this, sometimes considerably.