If we have a two electron system we can either have a singlet or triplet state.
The singlet state looks like
$$\chi=\frac{1}{\sqrt 2}(\chi_{+-}-\chi_{-+})$$
but we also have a triplet state in which
$$\chi=\frac{1}{\sqrt 2}(\chi_{+-}+\chi_{-+})$$
What is the physical difference between these two states due to the different phase factor?