In my set theory notes, one definition is:
Let $\langle A, < \rangle$ be a structure. $\langle A, < \rangle$ is a well-ordering if it is a well-founded linear ordering.
The problem is, nowhere in the notes does it mention what a linear ordering is. I can't find much online either so I wonder if it was meant to say "total ordering"?
Your guess is correct: "linear ordering" and "total ordering" are synonyms.