Homogeneity means that something is the same in every point in space, whereas isotropic means that there is no directionality. Uniformity implies there is "no variation".
But what is actually the difference between being homogeneous and uniform, e.g. for a field?
In my experience, 'homogeneous' is related to mixture, a property of a multi constituent body, and 'uniform' a property of a a single entity. Example: Eletric field can be uniform and a distribution of matter can be homogeneous.
In fact, the general meaning of 'homogeneous' is: of the same kind; alike; consisting of parts all of the same kind. And the general meaning of 'uniform': remaining the same in all cases and at all times; unchanging in form or character.
Similar to the answer of Nogueira and others comments.
It seems to me that homogeneity is used when matter is considered (tough, it can be in the presence of other components, as in cosmology) while uniformity has a more geometrical connotation. Therefore we use homogeneous for a mixture (meaning fine enough, if not a solution) or for a solid block with no cavities and uniform for a constant field, to give common examples.
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.
From my experience in different sciences, they mean the same thing but homogenous is typically used when there is a state change or an expected change to uniformity or current state is consistent throughout while uniform is usually used when no change in state is expected at all.
I think homogeneity means properties being the same at every point in space. Considering density as a property, it should also be the same at every point in space. So, a homogeneous system is uniform. By a uniform system, I mean a system whose density at every point in space is the same. https://en.wikipedia.org/wiki/Homogeneity_(physics)
