Two-photon excitation fluorescence (2PEF) and coherent anti-Stokes Raman scattering (CARS) are both third-order nonlinear optical processes, but for a long time, the true relationship and differences between them are not clearly understood. For decades, the second harmonic generation has been studied in conjunction with two-photon excitation fluorescence, so it was thought that the latter was a second-order nonlinear optical process. In order to make the two nonlinear interaction processes clear enough, the two nonlinear interaction processes are worthy to study at the same time. In this paper, firstly, we give the relationships between the 2PEF, CARS signal and their third-order nonlinear susceptibility, respectively; secondly, we use our own near infrared super-continuum CARS microscopy system to study both processes. In doing so, we describe the relationship between their third-order nonlinear susceptibility and the signal. The reconstructed images derived from CARS and those derived from 2PEF differ significantly when imaging the same 1.01 $\muup$m fluorescence polystyrene beads. If the lateral spatial resolution of the CARS imaging system is larger than the fluorescence polystyrene beads, the measured size cannot be used to calculate the real spatial resolution of the CARS system. However, the resolution of the 2PEF microscopy system can be obtained through the de-convolution of the 2PEF image, which is approximately equivalent to the current resolution of the CARS imaging system, which is measured using 280 nm polystyrene beads. The images of 280 nm polystyrene beads and 190 nm fluorescent polystyrene beads also exhibit differences between the two samples and the environment around them, respectively. This means that although CARS and 2PEF are both third-order nonlinear optical processes, they have their own properties. In particular, CARS is a third-order nonlinear optical oscillation process which is caused by the phasing match condition, but 2PEF is not influenced by the phasing match condition. The phase matching condition is responsible for the differences around the sample in the images of the 280 nm pure polystyrene beads, but not for the 190 nm fluorescent polystyrene beads. The de-convolution results for the 1.01 $\muup$m fluorescence polystyrene beads and the 280 nm pure polystyrene beads are very similar, so we can use the de-convolution results for 2PEF by the 1.01 $\muup$m fluorescence polystyrene beads to approximate the current measure condition and the resolution of the CARS imaging system. If we want to gain a more accurate resolution from the CARS imaging system, the spherical sample should be smaller than the lateral spatial resolution of this system.