# What do the “real” and “imaginary” parts of the Laplace and Z transform represent?

I've been able to wrap my head around the continuous and discrete Fourier transform just fine. I understand that the Fourier transform brings you from the time domain into frequency domain, and that the Fourier transform is just the Laplace transform but where $\sigma$, the real valued portion of $s = \sigma + j\omega$, is set to $0$. So if the imaginary portion, $\omega$, is the frequency, what does the real $\sigma$ represent?

Furthermore, why is it not like this between the DTFT and the Z transform? The DTFT is a specialized case not where $\sigma=0$, but where $r$ in $z=re^{j\omega}$ is set to $0$, i.e when $|z|=1$. Do the real and imaginary parts of the signal change what they represent in continuous and discrete signals?