We show that the star-forming regions in high-redshift luminous and ultraluminous infrared galaxies (LIRGs and ULIRGs) and submillimeter galaxies (SMGs) have similar physical scales to those in local normal star-forming galaxies. To first order, their higher infrared (IR) luminosities result from higher luminosity surface density. We also find a good correlation between the IR luminosity and IR luminosity surface density in starburst galaxies across over five orders of magnitude of IR luminosity from local normal galaxies to z ~ 2 SMGs. The intensely star-forming regions of local ULIRGs are significantly smaller than those in their high-redshift counterparts and hence diverge significantly from this correlation, indicating that the ULIRGs found locally are a different population from the high-redshift ULIRGs and SMGs. Based on this relationship, we suggest that luminosity surface density should serve as a more accurate indicator for the IR emitting environment, and hence the observable properties, of star-forming galaxies than their IR luminosity. We demonstrate this approach by showing that ULIRGs at z ~ 1 and a lensed galaxy at z ~ 2.5 exhibit aromatic features agreeing with local LIRGs that are an order of magnitude less luminous, but have similar IR luminosity surface density. A consequence of this relationship is that the aromatic emission strength in star-forming galaxies will appear to increase at z > 1 for a given IR luminosity compared to their local counterparts. ; Comment: Accepted for publication in The Astrophysical Journal; 13 pages, 7 figures; Online materials available at http://inthanon.as.arizona.edu/~wiphu/Rujopakarn_2010b