Quick definitions: Internal rim width is measured between the inner brake-track or bead walls, not the outer tire-to-tire measurement. A narrower internal width supports a narrower tire well; a wider internal width supports a wider tire with better support and a rounder profile at the same pressure.
What actually differs
Why wider rims followed wider tires, not the other way around
Research through the 2010s showed that wider road tires, at a given pressure, roll no slower and often faster than narrow ones, while being more comfortable and pinch-flat resistant. As tires widened from the archive-era 21-23mm standard toward today's common 25-30mm, rims needed to widen too, a narrow rim under a wide tire creates a lightbulb-shaped cross-section that hurts both aerodynamics and tire stability.
What this means if you're pairing new tires with an older archive-era wheel
A narrow archive-era rim, built for 21-23mm tires, can usually still mount a 25mm tire safely, but going much wider than that risks a poor tire shape and reduced stability. This is one of the more concrete reasons an older wheelset, even one in good mechanical condition, can hold a rider back from current tire width recommendations.
A 21mm internal rim fits you ifyou're running 25-30mm tires, which covers the large majority of current road setups, and you want the current mainstream standard without chasing the widest available option.
A 25mm+ internal rim fits you ifyou're running 28-32mm or wider tires for comfort or light gravel-adjacent riding, where the extra internal width keeps the tire properly supported and shaped.
