The wave always has a definite shape, and that's the fundamental truth about tbat particle. The state of the particle is just whatever the particle is doing. In other words, we make measurements, but we can't measure the wave directly. The information to answer the question is in the particle's state. Each allowable answer questions corresponds with the particle's state.
States are purely states of position.
If particles were always in pure states, quantum mechanics would be easy. Unfortunately, particles are rarely that simple. Often they exist in mixed states. It could be in a state that's 30 percent couch and 70 percent ceiling. But a problem arises when we ask the particle where it is.