nuances - What is the difference between -さ and -み suffixes to make a noun out of an adjective?

For example, both 悲しさ and 悲しみ are glossed as “sadness” in JMdict. What's the difference?

According to A Dictionary of Basic Japanese Grammar, 〜み “is more emotive and concrete characterization of some state”, while 〜さ “describes, in an analytical manner, the degree of state represented by an adjective”.

The book uses a few examples to highlight the difference, but I can't make sense of it.