I'm reading Combinatorics and Graph Theory, 2nd Ed., and am beginning to think the terms used in the book might be outdated. Check out the following passage:
If the vertices in a walk are distinct, then the walk is called a path. If the edges in a walk are distinct, then the walk is called a trail. In this way, every path is a trail, but not every trail is a path. Got it?
On the other hand, Wikipedia's glossary of graph theory terms defines trails and paths in the following manner:
A trail is a walk in which all the edges are distinct. A closed trail has been called a tour or circuit, but these are not universal, and the latter is often reserved for a regular subgraph of degree two.
Traditionally, a path referred to what is now usually known as an open walk. Nowadays, when stated without any qualification, a path is usually understood to be simple, meaning that no vertices (and thus no edges) are repeated.
Am I to understand that Combinatorics and Graph Theory, 2nd Ed. is using a now outdated definition of path, referring to what is now referred to as an open walk? What are the canonical definitions for the terms "walk", "path", and "trail"?