In Graph Theory, what is the difference between a tour and a trail? Are they the same thing? To my understanding, a tour is a walk with no repeated edges. I have found it hard to find a good definition for a trail, but the two seem very similar.
If they're the same, why have two terms for one thing?
Thanks in advance.
 A: All introductory graph theory textbooks that I've checked (Bollobas, Bondy and Murty, Diestel, West) define path, cycle, walk, and trail in almost the same way, and are consistent with Wikipedia's glossary. One point of ambiguity: it depends on your author whether the reverse of a path is the same path, or a different one.
I occasionally worry about people talking about paths and cycles and not assuming that they're simple, but graph theory textbooks don't do this (fortunately!).
It is not universal to define tour to begin with, and it's not done in a consistent way. I think that the motivation to do this is often: "Well, it's conventional to talk about Euler tours of a graph. Can we first define general tours, and then say that an Euler tour is a tour with some special property?" This leads to

*

*defining tours to be walks that traverse each edge at least once (Bondy and Murty)

*defining tours to be closed trails (Wikipedia)

*defining tours in the same way as trails (the source you consulted)

The word circuit is also ambiguous, though it most commonly means a closed trail.
A: Here's a book that defines walk, path (=walk with no repeated vertices), and trail (=walk with no repeated edges):
https://books.google.fr/books?id=vaXv_yhefG8C&pg=PA162&hl=de&source=gbs_selected_pages&cad=2#v=onepage&q&f=false
But it doesn't define tour. Incidentally, I feel like tour being used only for paths or trails where all vertices or edges are used.
