I'm a bit confused as to your question. Are you asking what those diagrams mean?
The energy oh a photon is proportional to its frequency. So increasing the frequency of the light is another way of saying you are increasing the energy of the photons.
The first diagram says that if you increase the energy of the photons continuously, you get a continuously increasing output current. In other words, no minimum step size. They are continuously proportional to each other.
The second diagram says they aren't. It says that to observe a flow of charge, the energy of the photons must exceed some threshold dependent on the sample material. In other words, there is a minimum photon energy required to produce eject electrons and produce current.
But I personally find the diagrams a bit lacking in that they do not seem to be comparing like-with-like since the first describes an charge response to a range of energies whereas the second diagram only describes the zero response and minimal non-zero response.
I also don't see how the second diagram necessarily implies that photon energies are discretized rather than electrons transition levels being discrete. It seems to me you only need either photons or electron transition states to be discrete to get a discrete response.
I thought that the concept for photons having discrete energies came from the math Planck had to do to working with blackbody radiation to solve the ultraviolet catastrope. Because integrating the photon energy levels across the blackbody radiation gave you infinities if it was continuous.
