What is the difference between the Edomites and the Amalekites? 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: &quot; ... 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.