Tropical mountains are global biodiversity hotspots, owing to a combination of high local species richness and turnover in species composition. Typically, the highest local richness and turnover levels are implicitly assumed to converge in the same mountain regions, resulting in extraordinary species richness at regional to global scales. We investigated this untested assumption using high-resolution distribution data for all 9,788 bird species found in 134 mountain regions worldwide. Contrary to expectations, the mountain regions with the highest local richness differed from those with the highest species turnover. This finding reflects dissimilarities in the regions' climates and habitat compositions. Forest habitats and humid tropical climates characterize the mountain regions with the highest local richness. In contrast, mountain regions with the highest turnover are generally colder with drier climates and have mostly open habitat types. The highest local species richness and turnover levels globally converge in only a few mountain regions with the greatest climate volumes and topographic heterogeneity, resulting in the most prominent global hotspots for avian biodiversity. These results underline that species-richness hotspots in tropical mountains arise from idiosyncratic levels of local species richness and turnover, a pattern that traditional analyses of overall regional species richness do not detect.