Soap scum vs scale what the two terms describe
Both come from hard water. Soap scum forms when soap reacts with the calcium in it; scale is calcium carbonate that can form when hard water is heated.
The difference, line by line
What it is
Soap scum: The product of soap reacting with calcium in hard water.
Scale: Solid deposits of calcium carbonate.
What makes it form
Soap scum: Soap meeting hard water, which is relatively high in calcium.
Scale: Heating hard water, as in a home water heater.
Hard water, step by step
What hardness means
The amount of dissolved calcium and magnesium in the water.
With soap: soap scum
In hard water, soap reacts with the calcium to form soap scum.
With heat: scale
When hard water is heated, solid deposits of calcium carbonate can form. This scale can shorten the life of equipment, raise the cost of heating water, lower the efficiency of electric water heaters and clog pipes.
What this doesn't tell you
What the deposit in your home is, how hard your water is, whether your water is safe, or how to clean or treat it. The heated-water example doesn't mean every scale deposit needs heat, and no cost, savings or equipment-life figure is given here.
Source
The four descriptions come from the USGS Water Science School.