It seems like Nubia and Kush sometimes get used interchangeably. It also seems like Ethiopia is just an ancient word for Africa south of Egypt... ? Is Nubia also a broad term or does it mean something specific? Is Meroe totally distinct or does it fall under some of the other words? I don't understand. Please assume I know nothing to help me untangle this.
The terms Nubia, Kush, and Ethiopia (in the ancient Greek sense) mean roughly the same geographical region, but in different time periods:
The term 'Kush' is first attested in Egyptian sources at the beginning of the Middle Kingdom (around 2000 BC). It's a general term referring to the region south of the first cataract (where modern Aswan is), but also used more specifically for the Egyptian-controlled area in modern Sudan in the 2nd millennium BC (controlled by the Viceroy of Kush). From the first millennium BC onwards, there was an independent kingdom of Kush.
Meroe is an ancient city in modern Sudan that was the capital of the kingdom of Kush from the 7th century BC to the 4th century AD.
Ethiopia is the Greek name for the kingdom of Kush (and more generally, for everything south of Egypt), but as geographical knowledge expanded, the term was also expanded to include the areas south of modern Sudan as well (aithiops in Greek means 'burnt-faced').
Nubia is the most 'modern' of these terms and refers to the same area (southern Egypt and Sudan). It is derived from the people who settled there after the end of the kingdom of Kush (called Noba or Nuba). What can be confusing is that many modern scholars refer to the region as Nubia also when they talk about antiquity (e.g., "the kingdom of Kush, in Nubia").
Hope this clears it up!