What is the difference between “length of days” and “long life?”

Answer:

A more literal translation of the verse is: "For length of days and years of life and peace they will add to you" (Proverbs 3:2 NASB). A similar statement is found later, "The fear of the LORD is the beginning of wisdom, And the knowledge of the Holy One is understanding. For by me your days will be multiplied, And years of life will be added to you" (Proverbs 9:10-11). Still, your question remains because there isn't much difference between "length of days" and "years of life." The contrast in "The fear of the LORD prolongs days, but the years of the wicked will be shortened" (Proverbs 10:27), shows terms "days" and "years" to be synonyms. We often find them used together in poetry:

"Are Your days like the days of a mortal man? Are Your years like the days of a mighty man?" (Job 10:5).

"I have considered the days of old, the years of ancient times" (Psalms 77:5).

"For all our days have passed away in your wrath. We bring our years to an end as a sigh. The days of our years are seventy, or even by reason of strength eighty years; yet their pride is but labor and sorrow, for it passes quickly, and we fly away" (Psalms 90:9 WEB).

"Years of life" is a phrase often used in the Old Testament to say how long a person lived: "These are the names of the sons of Levi according to their generations: Gershon, Kohath, and Merari. And the years of the life of Levi were one hundred and thirty-seven" (Exodus 6:16). Following wisdom increases how long we live on this earth. "Hear, my son, and receive my sayings, and the years of your life will be many" (Proverbs 4:10).

But sometimes the phrase is "days of life." "Here is what I have seen: It is good and fitting for one to eat and drink, and to enjoy the good of all his labor in which he toils under the sun all the days of his life which God gives him; for it is his heritage. ... For he will not dwell unduly on the days of his life, because God keeps him busy with the joy of his heart" (Ecclesiastes 5:18, 20).

"Length of days" puts more emphasis on how long someone lives, not just breathing, but in a productive fashion. Each day is put to full use and their number will be many, for God keeps a man busy.

"Wisdom is with aged men, and with length of days, understanding" (Job 12:12).

"That you may love the LORD your God, that you may obey His voice, and that you may cling to Him, for He is your life and the length of your days; and that you may dwell in the land which the LORD swore to your fathers, to Abraham, Isaac, and Jacob, to give them" (Deuteronomy 30:20).

"Length of days is in her right hand, in her left hand riches and honor" (Proverbs 3:16).

This is a poetic way of emphasizing a productive and long life.

In pointing out the various usage of "days" and "years" I had to pick through versions that rendered these words literally. Too often a translation will switch the words for another to make the meaning clearer.