Homogeneity is a property of composition. If a system is made of the same parts everywhere, then it is considered homogenous. Homogenity has to do with the smallest units that have identical composition or character. The central question here is one of identity. This allows a multi-component system to be described by homogeneity as well. Even a multi-component system can contain basic units with more than one element whereby the basic units are identical everywhere i.e. a unitary character. For instance, a substance consisting molecules is homogenous even though each molecule contains more than one atom. An important criteria for homogeneity is the scale of homogeneity. If you look at a susbtance containing molecules at the scale of an atom, then it is not homogenous, but if you evaluate at the molecular scale, then it is homogenous. The opposite of homogeneity is heterogeneity.
But uniformity is a property of concentration. A system is uniform if it (the population or the whole) is distributed everywhere in the same way. In other words, the concentration is the same everywhere. The opposite of uniformity is variability or dispersion.