We investigate two methods of measuring fitness in evolutionary games played among members of a finite population. Classical notions of stability account for the action of selection only, and use immediate reproductive gains as a measure of fitness. This classical interpretation of fitness is what we call reproductive fitness (RF), and is found in the early studies of evolutionary stability in finite populations. More recent work has incorporated the influence of random genetic drift by applying fixation probability (FP) as a measure of fitness. When defined in this way, fitness represents a measure of ultimate evolutionary success. Our main result describes an equivalence between candidate evolutionarily stable strategies under both the RF and FP interpretations of fitness. We apply this result to matrix games in which the use of mixed strategies is permitted, and find here an equivalence between the RF and FP conditions for evolutionary stability.