Why States’ vs. State’s? In the founding concept of American liberty, the primary purpose of government is to guarantee the rights of the people, which are derived from God. To accomplish this primary function of government, the power to govern was divided between a person’s State and The (several) States as a group (or the central government). States’ is the plural possessive. It references The States as a group and is thus the same as saying Federal Rights. So you could argue that people today who speak of States’ Rights have lost part of the basic concept before they even get started.
Why Rights vs. Powers? The second word of the phrase is also misused. Rights are given to the people by God, not to their State, a group of States, or to a central government. States do not have rights; they have powers to govern that have been granted by the sovereign people. That, Ladies and Gentlemen, is the concept of American liberty. Government at every level is supposed to execute only those powers for which the people have granted the authority. Any debate that begins with the “Rights” of any government at any level has most likely been lost from the outset. Even if the effort seems to have initial success, in the end it only winds up chipping away at our God-given Rights.
American liberty is rapidly approaching the cliff. It's up to you the citizen to change that direction if it's going to be changed. You have only this recourse at your disposal. Demand that all levels of government keep their hands off your God-given Rights unless the people grant them a Power to do so. Elect only those officials who are willing to abide by this restriction. Retire any elected official who abuses or usurps that which God has given you.
Arguing about which level of government will do a better job abusing your God-given Rights makes for interesting partisan battles, but it's a formula for failure year after year, election after election, and decade after decade -- as we have seen. After all, those who do not learn from history are doomed to repeat it. In summary: what was State’s Rights isn’t what it is today. What is States’ Rights isn’t what it was. What your Rights will be is up to you.