Second-order RLC transfer function

I solved the exercise in the picture with Laplace:

Not being familiar with systems theory yet, I do not understand one thing (circled in pink in the picture.)

The transfer function found with the black marker (tell me if it's correct) is \$ \frac{s}{s^2 + \frac{s}{RC} + \frac{1}{LC}}\$.

Theoretically it's the same as the transfer function written with the gray marker, \$ \frac{\omega_n^2}{s^2 + 2\varepsilon\omega_n s + \omega_n^2}\$, right?

If yes, then the natural frequency is equal to the square root of 1 or to the square root of 1/LC. Certainly a trivial question, but what I don't understand is just how to interpret the formula written with the gray marker.