particle physics - Breit-Wigner vs propagator?

Consider the two Feynman diagrams below:

I know for the second that we should use the Breit-wigner curve, but what about the first? If we go about using the propagator: \[\frac{1}{\tilde q^2-m_z^2c^2}\text{, (+ - - -) signature}\] then we a singularity when $\tilde q^2=m_z^2c^2$ which is subverted when the Breit-Wigner curve is used. Thus my question is as follows: When is it appropriate to use the propagator as given above and when to use the Breit-Wigner curve.