There's no term for music from the 16-bit console war era. The reason is that the music sounded very different due to the hardware capabilities and limits of each system.
There are many comparison videos between snes and genesis which can be used to compare audio.
From Castlevania, Simon's theme.
From Street Fighter 2, Blanka's theme and Ken's theme.
If there is one common technique that separates this music from the 8-bit era, it's "sampling".