In a nutshell, "Sin" is the fallen state that affects every human being on the planet. Thoughts, words, or deeds of disobedience are considered "sins," and the motivation behind our desire to engage in such wicked behavior is referred to as the state of "sin." In his well-known Psalm of confession, King David makes reference to his inherited sinfulness. In Psalm 51:5, notice that David refers to the word “sin” (singular).
To the Chief Musician. A Psalm of David when Nathan the prophet went to him, after he had gone in to Bathsheba. Have mercy upon me, O God, According to Your lovingkindness; According to the multitude of Your tender mercies, Blot out my transgressions. Wash me thoroughly from my iniquity, And cleanse me from my sin. For I acknowledge my transgressions, And my sin is always before me. Against You, You only, have I sinned, And done this evil in Your sight—That You may be found just when You speak, And blameless when You judge. Behold, I was brought forth in iniquity, And in sin my mother conceived me.- Psalm 51:1-5 (NKJV)
In verse 5, David is referring to the sin state in which he was born rather than any specific "sins."
The explanation of our fallen state is made clear in Romans 5:12:
Therefore, just as through one man sin entered the world, and death through sin, and thus death spread to all men, because all sinned — And in Romans 6:23, it is written: For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord. The price of sin is death.
As a result, we are born into sin (the fallen state) and commit acts of disobedience. We do not sin because we are sinners; rather, sin is what we do because we are sinners. We are all lost because of this. Because of the fatal condition of sin into which we are all born and which subsequently drives us to commit sins or disobey God's Word in our thoughts, words, and deeds, the world is condemned before God:
As it is written: "There is none righteous, no, not one; There is none who understands; There is none who seeks after God. for all have sinned and fall short of the glory of God, being justified freely by His grace through the redemption that is in Christ Jesus, whom God set forth as a propitiation by His blood, through faith, to demonstrate His righteousness, because in His forbearance God had passed over the sins that were previously committed, to demonstrate at the present time His righteousness, that He might be just and the justifier of the one who has faith in Jesus.- Romans 3:10-11,23-26
Without God's grace, there would be no hope for our situation. …
But God, who is rich in mercy, because of His great love with which He loved us, even when we were dead in trespasses, made us alive together with Christ (by grace you have been saved), and raised us up together, and made us sit together in the heavenly places in Christ Jesus, that in the ages to come He might show the exceeding riches of His grace in His kindness toward us in Christ Jesus. For by grace you have been saved through faith, and that not of yourselves; it is the gift of God, not of works, lest anyone should boast.
- Ephesians 2:4-9
For He made Him who knew no sin to be sin for us, that we might become the righteousness of God in Him.
- 2 Corinthians 5:21