What matters is the gauge (diameter), turns count, and sometimes that the wrap style be the same. AFAIK the color is an arbitrary addition to the lacquer coating the wire....It is mostly there to make identifying defects to the insulating lacquer easier.
Application and frequency may make aspects more critical. I've been able to rewind 30's Philco antenna and osc transformer coils with a different (thicker) gauge and the same turns count and had them work.
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