On terms "Orientation" & "Oriented" in different mathematical areas?

Question

The goal of this question is to help to deal with different meanings of the words such as "orientation" and "oriented" in different mathematical areas.

Are different oriented concepts somehow related to each other in different mathematical areas?

1. Oriented matroids (Matroid Theory)

2. Oriented graphs (Graph Theory)

3. Orientation (Topology, Global Analysis)

4. Other areas?

Answer 1

I outline some graph theory and matroids where orientation occurs in the terms such as oriented matroids and oriented graphs.

Distinctions

1. Are Oriented Graphs Related to Oriented Matroids?

1.1. Intuitive explation for oriented matroids? (with oriented matroids and digraphs question)

1.2. What is the analogous duality theorem between the cuts and cycles related to Matroids?