We are now considering states that are labeled by where they are located.
For example, state means that the particle is located at . In other words, we are considering wave functions that are on a real line.
Now, let us first consider the scenario that there is only one particle locating at . It is totally fine to change the name of the location to, for example, . In this sense, we may say that the two representations of this particle and are equivalent! Technically, we are in a space that is translationally-invariant. So relabelling does not change the physics.
Let us now consider two particles. Particle is in the state of and particle is in the superposition . In other words, we are now considering a composite system if we omit the normalizing factor.