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

Question

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.

Answer 1

They both mean the same thing but the nuance is as follows:

〜さ (as in 悲しさ、楽しさ、痛さ) indicates a degree or an amount of 〜
〜み (as in 悲しみ、楽しみ、痛み）indicates a state of being

I find the following contrasting examples as definitive:

A:「痛さはどれくらいですか？」 = implies amount

B:「痛みの程はどれくらいですか？」 = we add 程{ほど} to indicate an amount

However, to make things easier (or harder) B is starting to imply "an amount" too (I'll see if I can find an example).

My supposition is that A was originally "the correct way", but so many people used the incorrect way that it is becoming correct; just like in English, meh!

On OKWave I found the following useful examples:

「痛み」：　痛むこと、痛んでいる状態にあること = Pain, in a state of pain 
「痛さ」：　どれだけ痛んでいるかの状態・程度 = A state indicating how much pain, an amount

○「私達の心の痛みがわかりますか」＝「私達の心が痛んでいることがわかりますか」
   => Do you understand that our hearts are pained (by this)?

○「私達の心の痛さがわかりますか」＝「私達の心がどれだけ痛んでいるかがわかりますか」
   => Do you understand exactly how much our hearts are pained (by this)?

△「かなりの痛みだ」(NG)
○「かなりの痛さだ」＝ very painful

○「かなりの痛みがある」＝ very painful
△「かなりの痛さがある」 (NG)

Note, preceding「がある」the most appropriate option is「痛み」.

○「軽い痛みがある」＝ a little painful
△「軽い痛さがある」 (NG)

(Source: http://okwave.jp/qa/q6754018.html)

Answer 2

〜さ seems to describe a "measurable" amount, while 〜み seems to describe a general concept of the adjective.

• 悲しみ - the general concept of sadness
  
• 映画の悲しさ - the (amount of) sadness of that movie (possibly compared to other movies).

That's how I tend to compare them.

Also note that many of these types of adjective have corresponding verbs, such as 悲しむ、楽しむ、痛む. The ～み　is just the stem of the ～ます form, which is often used as a noun. So this might help distinguish them a little. For example:

帰り (the return), 踊り (a dance), 痛み (a pain), 楽しみ (enjoyment, fun)

Answer 3

the 悲しみ　version could be re-written as 悲しく感じ, though not 100% accurate is a way to easily remember what the meaning is. This would be the feeling of sadness.

さ i like to liken to 差, which means difference or level. So 悲しさ would be level of sadness