Esau is considered the ancestor of the Edomites. He is also the grandfather of Amalek. According to the Book of Genesis, Amalek was the son of Eliphaz and his concubine Timna. Eliphaz was the first-born son of Esau by his wife Adah. Amalek is considered the ancestor of Amalekites. Are the Amalekites and Edomites different names for the same tribe? Or are the Edomites a different tribe with a separate lineage to Esau?
I think you've mostly answered your own question. Esau is the father of the Edomites and Amalek (grandson of Esau) is the father of the Amalekites.
Genesis 36:9 ESV These are the generations of Esau the father of the Edomites in the hill country of Seir.
Genesis 36:12 ESV Timna was a concubine of Eliphaz, Esau's son; she bore Amalek to Eliphaz.
Furthermore, they are each described as doing different things to Israel following Israel's time at Meribah. This adds proof to the argument that they're distinct tribes.
Exodus 17:7,8,13 And he called the name of the place Massah and Meribah, because of the quarreling of the people of Israel, and because they tested the Lord by saying, “Is the Lord among us or not?” Then Amalek came and fought with Israel at Rephidim. ... And Joshua overwhelmed Amalek and his people with the sword.
Numbers 20:13,14,21 ESV These are the waters of Meribah, where the people of Israel quarreled with the Lord, and through them he showed himself holy. Moses sent messengers from Kadesh to the king of Edom: " ... Please let us pass through your land. We will not pass through field or vineyard, or drink water from a well. We will go along the King's Highway. We will not turn aside to the right hand or to the left until we have passed through your territory.” ... Thus Edom refused to give Israel passage through his territory, so Israel turned away from him.
Esau was the progenitor of the Edomites. Pretty straightforward.
Now whilst Amalek was indeed the grandson of Esau, who later had children of his own called the Amalekites, there existed another "Amalek".
These Amalekites were one of the many ancient inhabitants of the Levant and when the word "ancient" is used in Old Testament, it REALLY means ancient. Between the antediluvian (pre-Flood) era and the pre-calling era (time span between the Tower of Babel's creation and Abraham's calling), more specifically.
Were they one of the Nephilim hybrids that spawned after the Flood (Genesis 6:4), considering the Bible's consistently negative portrayal of Amalek? You decide.
Yet we, as 21st century individuals, like to believe that Abraham and his family were super ancient people.
The distinction was clearly evident in these verses:
"And they returned, and came to Enmishpat, which is Kadesh, and smote all the country of the Amalekites, and also the Amorites, that dwelt in Hazezontamar."- Genesis 14:7. THIS WAS WAY BEFORE ESAU'S GRANDSON AMALEK WAS BORN.
"And David and his men went up, and invaded the Geshurites, and the Gezrites, and the Amalekites: for those nations were of old the inhabitants of the land, as thou goest to Shur, even unto the land of Egypt."- 1 Samuel 27:8 (Again, Esau as the descendant of Abraham wouldn't be considered "ancient" by Biblical standards so neither would his own descendants be considered that way).
Though they were different groups, spawned from different time frames, they were united by one common desire: the annihilation of Israel in its entirety. Their lives were centered around despising God's chosen people and attacking anything related to them. That was why Haman was called an Agagite, the term used to describe Amalekite kings, even though the physical nation of Amalek was long extinct before Haman was even born (1 Chronicles 4:43).
The hatred of Jacob truly ran deep in Esau's line to name your kid that way.