The answer is that it depends.
If we consider a transition between energy levels in an atom then the initial and final energies are well defined. So for example in the $1s \to 2p$ transition in a hydrogen atom the difference in the energy states is $10.2$ eV. So a $10.2$ eV photon can be absorbed to excite the electron and the relaxation process emits a $10.2$ eV photon.
But in ionisation the final energy of the electron can have any value. The initial energy is well defined, but the ejected electron can have any speed from zero up to however much energy is available so for hydrogen any photon with an energy of greater than $13.6$ eV can be absorbed to cause ionisation.
Sometimes the incoming photon is completely absorbed so only an electron is emitted. However we can also have a process called Compton scattering where the incoming photon is absorbed and the electron plus a lower energy photon is emitted. In effect the incoming photon only transfers part of its energy to the electron so a lower energy photon is still present along with the ionised electron.