Consider a continuous X-ray photon and a characteristic X-ray...

Continuous X-rays are produced due to the deceleration of fast-moving electrons when they strike a heavy target (Bremsstrahlung effect).

Characteristic X-rays are produced when an inner-shell electron is knocked out of an atom by a high-energy electron, and an outer-shell electron transitions to fill the vacancy, emitting an X-ray photon.

Since both photons have the same wavelength $\lambda$, their frequency $\nu = \dfrac{c}{\lambda}$ and energy $E = \dfrac{hc}{\lambda}$ are identical.

Penetrating power depends on the energy of the photon, so it is also the same for both.

Thus, only the method of creation differs between the two photons.