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

Question

Example 悲しさ is sadness, and 悲しみ is sadness too. What is the difference? According to Dictionary of Basic Japanese Grammar, -み "is more emotive and concrete characterization of some state" and -さ "describes, in an analytical manner, the degree of state represented by an adjective". The book a a few examples to highlight the difference, but I couldn'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