If you use or come across the term 'order of magnitude' in writing, how do you interpret it?

E.g., "These two values differ by an order of magnitude."
#SciComm #ScienceWriting

I have ALWAYS interpreted 'order of magnitude' to have a very specific meaning: that a number differs by a power of 10.

E.g., 1,000,000 is 3 orders of magnitude greater than 1,000.

I was reading part of a writing style manual (if that tells you anything about how my day is going), and I came across a recommendation on using 'order of magnitude.' Specifically, don't use it, because it is a cliche meaning "by quite a lot." This upsets me!