Both health inequalities and social group health differences are important aspects of measuring population health. Despite widespread recognition of their magnitude in many high- and low-income countries, there is considerable debate about the meaning and measurement of health inequalities, social group health differences and inequities. The lack of standard definitions, measurement strategies and indicators has and will continue to limit comparisons--between and within countries, and over time--of health inequalities, and perhaps more importantly comparative analyses of their determinants. Such comparative work, however, will be essential to find effective policies for governments to reduce health inequalities. This article addresses the question of whether we should be measuring health inequalities or social group health differences. To help clarify the strengths and weaknesses of these two approaches, we review some of the major arguments for and against each of them.