I had the same problem. What seemed to set them firmly apart was the connection to a LADDER.
Ladder jives with the word latitude. So the lines of latitude are like climbing the rungs of a ladder. And the values of latitude are how high up (or down) you are.
Generally I just go with that, it automatically defines the other term... but if you do want to go further with longitude, I agree that using terms with LONG do the job. To get the longitude, you go ALONG the rungs LONGWAYS. The vertical lines are the hashmarks to show how far you've come along.
I'm convinced in my years thinking about this personally and then teaching that a big part of the challenge of any imagery/phrases is the confusion between whether you're talking about the line itself or values. It surely confused me to no end that values of latitude were north/south, while the lines of latitude were drawn east-west. I think/hope the ladder/latitude connection is a clear way to help people of all ages overcome the confusion.