I agree that this usage is very confusing. Here is a sloppy collage I made to try and explain the difference.
All of the pictures here could be called "a scale" in a general sense. For example, if I said, "Weigh it on a scale!" any of these tools would be appropriate.
However, the top row here depicts some scales or a set of scales If the weighing tool has two or more parts to balance (like the top row), you can refer to it as the scales or a scale. The middle image is the plural form of scales, while the scales in the first image could be considered a noun with no singular form.
The bottom row depicts a specific scale.If you're in the gym, the more common usage is the version without the -s, scale: "Step on the scale in the corner."
For context, I am a young, Midwestern American. Older folks or other countries might use scales instead.