Many clades contain ecologically and phenotypically similar species across continents, yet the processes generating this similarity are largely unstudied, leaving fundamental questions unanswered. Is similarity in morphology and performance across assemblages caused by evolutionary convergence or by biogeographic dispersal of evolutionarily conserved ecotypes? Does convergence to new ecological conditions erase evidence of past adaptation? Here, we analyse ecology, morphology and performance in frog assemblages from three continents (Asia, Australia and South America), assessing the importance of dispersal and convergent evolution in explaining similarity across regions. We find three striking results. First, species using the same microhabitat type are highly similar in morphology and performance across both clades and continents. Second, some species on different continents owe their similarity to dispersal and evolutionary conservatism (rather than evolutionary convergence), even over vast temporal and spatial scales. Third, in one case, an ecologically specialized ancestor radiated into diverse ecotypes that have converged with those on other continents, largely erasing traces of past adaptation to their ancestral ecology. Overall, our study highlights the roles of both evolutionary conservatism and convergence in explaining similarity in species traits over large spatial and temporal scales and demonstrates a statistical framework for addressing these questions in other systems.