The Hebrew chattah (חַטָּא) is an intensive form derived from chata (H2398, to sin, miss the mark). As an adjective it means sinful; as a noun, sinner — one characterized by habitual sin or notorious sinfulness.
While cheta (sin) is the act, chattah is the characterization — the person known for sin. This word appears in the famous address to Moses: 'Must we die? We are lost, we are all lost! Anyone who even comes near the tabernacle of the LORD will die. Are we all going to die?' (Numbers 17:12-13). Psalm 1 opens with the way of the resha'im (wicked) contrasted with the righteous — the Psalms' entire wisdom framework rests on understanding what it means to be a chattah vs. a tzaddik. Recognition of one's sinfulness is the beginning of the journey to God.