In this study, we characterized the variations in ionospheric irregularities and medium-scale traveling ionospheric disturbances (MSTIDs) simultaneously at mid-latitudes over central China based on high-fidelity observations of the total electron content (TEC) from a Beidou geostationary satellite and explored their quantitative relationships during 2016–2017. Ionospheric irregularities generally occurred during 20:00–03:00 local time (LT) in summer and reached a peak rate of ~30% at night; during the daytime in summer, the irregularities had a weak occurrence peak of not more than ~10%. The occurrence rate of nighttime MSTIDs showed a major peak of ~45% in summer and a secondary peak of ~20% in winter, whereas the main peak in winter was ~30% during the daytime. Additionally, the period, velocity, wavelength, and propagation direction of nighttime MSTIDs were different from those of daytime MSTIDs. There was a strong correlation between ionospheric irregularities and MSTIDs at night when the rate of ionospheric irregularities occurring during MSTIDs reached 90%. However, the situation during the daytime was different; the rate of ionospheric irregularities associated with MSTIDs did not exceed ~20%. These results indicate that nighttime MSTIDs could play an important role in producing ionospheric irregularities, but daytime MSTIDs do not. The different diurnal relationships between ionospheric irregularities and MSTIDs can be attributed to the different generation processes of MSTIDs. Our results from Beidou GEO TEC observations provide a new perspective for understanding ionospheric irregularities and MSTIDs and their quantitative relationships.