[freedumb2003]

In conclusion, the distinction is in the complexity of the idea, and certainly not a measure of uncertainty as is sometimes misconstrued by laypeople.

I am sorry, but you are not quite right. A Scientific Theory attempts to explain phenomena. Laws are data points within the framework of a theory.

[js1138]

Facts are data points (or broad undisputed statements, such as the earth revolves around the sun). Laws are (generally mathematical) statements of relationships among data points, such as Newton's laws. Theories are, as you say, explanatations.