What is the difference between Matru Navami and Avidhava Navami?

They are different names for the same observance. Matru Navami emphasises the mother aspect — it is the Shradh day of all deceased mothers. Avidhava Navami specifically refers to women who died while their husbands were still living (avidhava = not-widow). Both names describe the same ninth tithi Shradh during Pitru Paksha. The dual name reflects the two populations this day serves: mothers in general, and specifically wives who predeceased their husbands.