We study the brightness and the color variabilities of 34 red and 122 typical quasi-stellar objects (QSOs) at z = 0.3-1.2 using data from the Pan-STARRS Medium Deep Survey. The red and the typical QSOs are selected based on the ratios of the flux densities at 3000 Å to those at 4000 Å in the rest frame. We find that 16 out of 34 red QSOs are identified as extended sources, which exhibit strong brightness and color variabilities at shorter wavelengths due to the contamination of the emission from their host galaxies. Some point-like QSOs with significant color variabilities are able to change their color classification according to our spectral definition. The timescales of the color variabilities for these point-like QSOs are within 4 years, suggesting that the size scales of the mechanisms producing the color variabilities are less than a few light years. The spectra of some extended and point-like red QSOs can be well fitted with the dust-reddened spectra of a typical QSO, while others are difficult to explain with dust reddening.