Intuition for resonant, natural, and oscillatory frequencies of RLC circuits?
There are quite a few subtle differences between band-pass and low/high filters but, for a simple LCR band-pass filter, damped and un-damped resonant frequencies are the same numerically and formulaically, \$\dfrac{1}{2\pi\sqrt{LC}}\$. 

This is also the (un-damped) natural resonant frequency for high/low pass filters.

When damping is added, the natural frequency stays the same but it can (eg for a low pass filter) rotate anticlockwise in the pole zero plane and this leaves (in the jw axis) what is known as the damped resonant frequency, \$\omega_d = \omega_n\sqrt{1 - \zeta^2}\$. See lower part of 1st set of pictures below (it's basically Pythagoras and right-angle triangles).

And for low pass filters, there is the frequency at which peaking occurs and this is slightly different to damped resonant frequency, \$\omega_p = \omega_n\sqrt{1 - 2\zeta^2}\$.

The amplitude that this peaks at is \$\dfrac{1}{2\zeta\sqrt{1-\zeta^2}}\$



The proof of these three different frequencies for a low-pass filter is relatively straightforward but a little long winded. Below is an extract of a design paper for a 2nd order low pass filter where it is shown that a varying Q-factor moved the "peaking" frequency away from the natural frequency (100 Hz in this example) but, as always Q is the value of the peak at the natural resonant frequency: -



Maybe a close up view will be more exciting: -