Ultrafast phenomena and dynamics have been a rapidly developing field of condensed matter physics in recent years. "Ultrafast condensed matter physics" aims to study the ultrafast dynamics of quantum materials in the excited state and non-equilibrium state, thus revealing the intrinsic properties and realizing control of the quantum states. It employs ultrafast light pulses to excite the condensed matter, in ultrahigh temporal resolution, and detect the emitted photons or electrons. With the development of this field, many new physical concepts about electrons have emerged, which are different from conventional electrons in equilibrium states. Accurately understanding, defining, and classifying these concepts are becoming increasingly important for the development of ultrafast condensed matter physics research. Taking the ultrafast quasiparticle relaxation process as an example, we classify and compare the similarities and differences of photo-carrier, laser-heated electron, hot electron, thermal electron, photo-electron, etc. The classification also involves many physical concepts of the states, such as ground state, excited state, non-equilibrium state, transient state, metastable state, hidden quantum state, steady state, and equilibrium state. Using the different natural forms of water as an analogy, we illustrate the similarities and differences of the above concepts vividly. Our work may facilitate colleagues in understanding these concepts, and pave a way for the smooth development of ultrafast condensed matter physics. The ultrafast relaxation process of non-equilibrium state carriers (including electrons, holes, excitons, etc.) occurs on the time scale of femtosecond to nanosecond. In analogy to the circulation of water between the sea and sky, we vividly understand several important concepts of the carrier types, and clearly distinguish them. Specifically, by absorbing the photon energy, valance electrons are excited to become the photo-carriers, which are far above the Fermi surface. Such excited states are non-equilibrium states. The excited state photo-carriers will relax, during which the electrons exchange energy with lattice phonons and other types of elementary excitations, if any. The photo carriers have a separate temperature from that of the lattice. Upon relaxation, when they reach thermal equilibrium with local lattice ions, they become laser-heated electrons. When the laser-heated electrons further exchange energy with a wider range of lattice ions, the temperature is reduced and they become hot electrons. Finally, when the electrons thermalize with a wider range of lattice ions to assume ambient temperature, they become thermal electrons. Note that photo-carriers do not satisfy the Fermi-Dirac distribution. This is very different from the laser-heated electrons, hot electrons, or thermal electrons. The relaxation process includes but is not limited to electron-phonon coupling and phonon-phonon scattering. Photo-carriers may have coherence among them, but the other three concepts do not, as reflected by their names (heat, hot, thermal, etc.). Although laser-heated electrons and hot electrons also belong to excited state electrons to a certain extent, excited state electrons in ultrafast spectroscopy refer more to photo-carriers. The concept of laser-heated electrons emphasizes that electrons are heated by light excitation, while hot electrons emphasize that the electron temperature is higher than the ambient temperature, and electrons that are excited by other forms (such as electric fields) can also be called hot electrons. Thermal electrons are obtained from the ambient finite temperature and do not require external heating. The biggest difference between hot electrons and thermal electrons is whether the temperature is higher than the ambient temperature. Thermal electrons can be regarded as ground state electrons to some extent. Photo electrons have energies large enough to escape the solid.
