The relationship between the continuum intensities and magnetic fields for stable and decaying sunspots is analyzed using the scattered-light-corrected data from the Helioseismic and Magnetic Imager. From our analysis, the main differences between stable and decaying sunspots are as follows. In the continuum intensity range from 0.35I (qs) to 0.65I (qs), where I (qs) is the continuum intensity of the quiet solar surface, the relationship between continuum intensity and transverse magnetic field and the relationship between continuum intensity and inclination display a much higher scatter during the decaying phase of the sunspots. During and after the formation of the light bridge, the scatter plots show a bifurcation that indicates that the two umbrae separated by the light bridge have different thermodynamic properties. The continuum intensity of the umbra in a decaying sunspot is brighter than that of the stable sunspot, indicating that the temperatures in the umbra of decaying sunspots are higher. Furthermore, our results show that the mean continuum intensity of the umbra gradually increases during the decay of the sunspot, but the mean continuum intensity of the penumbra remains constant. Simultaneously, the vertical and transverse magnetic field strengths in the umbra gradually decrease, and the vertical magnetic field strengths in the penumbra gradually increase. The changes in the umbra occur earlier than the changes in the penumbra of the decaying sunspot, suggesting that the umbral and penumbral decay may be an interdependent process during the decay of the sunspot.