Inequity means (1) injustice or unfairness, or (2) an instance of injustice or unfairness. It’s an antonym of equity, which denotes justice, fairness, or balance.
Iniquity is closely related—both words ultimately derive from the Latin aequus, meaning equal—but it refers to extreme injustices, gross immorality, or acts regarded as sinful. An inequity may be a minor injustice or a small instance of unfairness, while iniquities are by definition very large or especially heinous.
Iniquity appears often in the phrase den of iniquity, referring to a place where immoral or wicked things happen.