If you drive from Texas to New York, you do not become a second-class citizen the moment you cross the state line. Article IV, Section 2 of the Constitution guarantees that "the Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States." This clause prevents states from discriminating against residents of other states when it comes to fundamental rights like earning a living, owning property, or accessing the courts.
The Supreme Court has said this clause "was to help fuse into one Nation a collection of independent, sovereign States." In practice, it means New Jersey cannot charge out-of-state commercial fishermen higher licensing fees just because they live in Delaware, and Alaska cannot reserve high-paying jobs exclusively for Alaskans. States can draw some distinctions -- they can charge nonresidents higher tuition at public universities, for example -- but only for activities that are not considered fundamental. The test is whether the discrimination involves a right so basic that denying it would undermine national unity. This is separate from the Fourteenth Amendment's Privileges or Immunities Clause, which protects rights of national citizenship and has a very different legal history.