Inequality, bi-polarization and polarization are related but distinct concepts aiming at analysing the income distribution. This paper first recalls the main differences between these three notions of inequality, bipolarization and polarization and then suggests using the so-called Shapley decomposition to show that the various income sources have a different impact on these three types of indicators. Our empirical investigation, based on 2008 data for Luxembourg, shows in fact that, in the case of the so-called zero income Shapley decomposition, inequality in Luxembourg is strongly related to income from capital while bi-polarization is mainly due to the distribution of income from work and polarization to that of the income from work and transfers.