Studies based on Hubble Space Telescope (HST) photometry in F275W, F336W, and F438W have shown that the incidence and complexity of multiple populations (MPs) in globular clusters (GCs) depend on cluster mass. This result, however, is based on nearby, low-reddening Galactic GCs, for which we can obtain accurate F275W photometry. In this work, we exploit HST photometry in F336W, F438W, and F814W to characterize MPs in 68 Galactic and extragalactic GCs by using the pseudocolor C F336W,F438W,F814W, which is more efficient in terms of observation time than the pseudocolor C F275W,F336W,F438W adopted in previous works. We first analyze the Galactic GCs alone and find that the red giant branch (RGB) color width strongly correlates with [Fe/H]. After removing the dependence from metallicity, we obtain a strong correlation with cluster mass, thus confirming previous findings. We then exploit the RGB width to compare MPs in Galactic and extragalactic GCs. Similarly to Galactic GCs, the RGB width of Magellanic Cloud (MC) GCs correlates with cluster mass after removing the dependence from metallicity. This fact demonstrates that cluster mass is the main factor affecting the properties of MPs. The MC clusters exhibit, on average, narrower RGBs than Galactic GCs with similar mass and metallicity. We suggest that this difference is a signature of stellar mass loss in Galactic GCs. As an alternative, the mass-RGB-width relation would depend on the host galaxy. Finally, we use ground-based photometry to investigate Terzan 7 through the $C{U,B,I}$ pseudocolor, ground-based analogs of $C{F336W,F438W,F814W}$ and find that this cluster is consistent with a simple population.