Why are relationships among flash and ambient expressed as percentages like 10% but among main and fill expressed as ratios like 3 to 1?
Lighting ratios are a simple comparison of two light sources on the subject. Most often it is the main and fill light being compared, but the ratios can also be used to describe the relationship of accent lights to the primary illumination. The metering and mastery of ratios was important to film photographers who were using controlled lighting for two main reasons.
The information above can be defended as fact. What follows is admittedly conjecture, although I believe both these points to be true.
The ambient-to-flash comparison is, in part, more appropriately expressed as a percentage because they are most often coincidental means of lighting. (Coincidental = done or happening by chance, happening or existing at the same time.) The "main" light tends to be whatever amount or direction of illumination is available, and the "fill" light is often direct or diffused flash at or near the camera.
Percentages are also used because they are easier to comprehend and simpler to express in a digital read-out. (An 8:1 ratio is a difference of three stops between the main and fill light, which is more confusing than saying the fill light can be expressed as 11% of the overall exposure.)