What is the difference between a path and a route in graph theory?

Question

Counts

A route in a graph is an alternating sequence of vertices and edges in which any two adjacent elements are incident.
A path is a sequence of edges (in an undirected graph) and/or arcs (in a directed graph), such that the end of one arc (edge) is the beginning of another arc (edge).
I don’t understand what the difference is, for me it’s the same thing, or am I still not understanding something?

Answer 1

According to Kuznetsov O.P. Discrete Mathematics for Engineers 1980: a more general definition of a route, given in section 4-2, the notion of a path is introduced for directed graphs, section 4-4

Answer 2

I myself taught Graph Theory quite a long time ago, I don't remember everything. Judging by the search results on the web, there are different interpretations:
- the route and the paths are, in fact, the same thing...
- the path is a special case of the route, but not containing repeating edges..
There was something else....
If we take the wording of your question verbatim, then the route is a subgraph of the original graph, with vertices and edges, and the path is a set of ONLY edges ... I don’t think this is correct, but it’s written that way.

Answer 3

Here's what google suggested:

A route is called open if its end vertices are different, and closed or cyclic otherwise.
An open route is called a chain if all edges in it are different (vertices can be repeated).
A path in which no vertices are repeated is called a path (simple path).

It follows that a path is a part of a route that does not contain edges between repeated vertices.
Definitions spied here https://studopedia.ru/3_80680_marshruti-puti-i-tsi...