Who is talking about equity vs equality?

Yesterday I was in a discussion about equity, and the person who brought up the topic compared it to equality. My guess is equity is a liberal concept, but I couldn’t help think about the conservatives I know who over the years have said to me people aren’t equal. They said it in the context of communists treat everyone equally. I felt at the time it was a subtle part of their rhetoric against Democratic candidates who often talk about equality in the country. I’m in the US.

Straighten me out. Am I overthinking?