As one alloy of copper, bronze shares many of its base metal's characteristics. Indeed, the distinction between the two as names of colors, although significant, may seem slight. Both colors have definite yellow, orange and red tones; this can make them hard to distinguish. But upon closer study and comparison, the distinctions between the colors of bronze and copper become clear.
As Metals
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Copper is its own element, while bronze is composed of copper alloyed with tin. Because of this, the colors of the two metals differ slightly when "raw." Bronze may have a deeper, yellow-brown tone than copper, which may appear more red-pink overall. The difference in their chemical composition directly affects the difference in their visual appearance.
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As Patinas
Bronze and copper, as metals, can be turned any number of different colors, from white to black, by the use of patinas. However, chemical formulas react differently to each type of metal, so a patina formula to turn bronze yellow must be a different formula from that used to turn copper yellow. Alternatively, a formula to blacken bronze may bring out a green tint in copper. Finally, the "natural" patina of each metal, formed by slow oxidation, differs slightly. Copper by itself turns green and grey, called "verdigris," because of copper oxide. Meanwhile, bronze turns brown much faster, because of the tin in its alloy, although it can also turn green. Both metals' patina colors deepen and enrich over time.
In Paint
Generally speaking, copper contains more pink tones than does bronze, which contains more brown tones. However, formulas or proportions for making bronze and copper colors out of paint vary widely. They depend upon the kind of paint used, such as oil or latex bases; they also depend upon the brand of paints used, the inclusion or exclusion of metallic particles, and the ultimate purpose of the paint -- for example, whether you want to paint a car, an antique, some hardware or a picture on canvas. For hobbyists, both bronze and copper are available as labeled, pre-mixed colors, in small amounts.
As Digital (RGB) Color Patterns
When constructed for computer screens, the colors' difference becomes numerically clear: bronze is "more red" than copper in this situation, which does not tend to include a value for yellow. Specifically, the color of copper requires proportions of 184 Red, 115 Green, and 51 Blue parts. By contrast, bronze requires 205 Red, 127 Green, and 50 Blue parts. This slight difference can be replicated accurately on any computer system with at least a 24-bit color screen.