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The distances to four galaxies and two globular clusters which are derived with the aid of period-luminosity and period-color relations of δ Scuti and SX Phe stars are compared to the distances derived by other methods, in particular RR Lyrae stars. We examine the luminosities of horizontal branch or RR Lyrae stars in Oosterhoff I and II globular clusters. Observational data from a variety of sources indicate a discontinuous jump of ∼0.2 mag in the luminosities of RR Lyrae variables at [Fe/H] ~ -1.5 as we transition from Oosterhoff I to Oosterhoff II clusters. If Oosterhoff I clusters have RR Lyrae variables with average M_V values of M_V= 0.53 mag at [Fe/H] = -1.5, it implies that RR Lyrae stars in Oosterhoff II clusters average M _V values are ∼0.34 mag. Unlike the Oosterhoff I clusters which show an increase in the V luminosity of RR Lyrae stars as [Fe/H] becomes smaller, little or no change in the V luminosity of RR Lyrae variables is evident in Oosterhoff II clusters in the interval of [Fe/H] from -1.5 to -2.2. We find distance moduli found with RR Lyrae variables agree to ≤ 0.04 mag with those found with the δ Scuti and/or SX Phe variables if the M _V values of RR Lyrae stars above are adopted. We find evidence of recent star formation (presence of near solar-metallicity δ Scuti stars with ages of 150 Myr to 1 Gyr) in the Large Magellanic Cloud (LMC), Small Magellanic Cloud, and the central region of the Fornax (dSph) galaxies. We also find an older population of metal-poor δ Scuti variables (SX Phe stars) in the LMC and Fornax galaxies. The Carina dSph is unique in that only an old population of metal-poor δ Scuti variables is evident. No evidence of recent δ Scuti star formation is found. The minimum periods observed for the SX Phe variables (blue stragglers) in the globular clusters M55 and ω Cen indicate that they could have been formed in a burst of metal-poor single star formation in the last 2.9-6 Gyr. If formed by the more acceptable scenario of stellar mergers, it is likely that the merged remnant resembles a normal star in a relatively advanced stage of main-sequence evolution with an enriched He core and ordinary He envelope. We present equations to calculate intrinsic-color indices for δ Scuti, SX Phe, and RR Lyrae stars at mean light. Finally, we show that the fundamental-radial-pulsating stars (δ Sct and SX Phe variables) have larger average light amplitudes than the first-overtone pulsating variables. The fundamental metal-poor variables (SX Phe stars) have the largest average and individual amplitudes.