This might change depending of what discipline you are investigating but:

- **homogeneous**: refers to a material that you cannot distinguish different phases in it.  Usually it refers to the density properties, and it's an indicator that the density is uniform when you look at it at various scales (from m to sub mm). 

(some etymology: the word comes from the greek "**ομογενής**", which means "the one who comes from the same breed/genealogy/group"). 

- **isotropic** usually refers to the mechanical properties. 

(again some etymology: the word comes from the greek "**ισο-τροπος**". **ισο** means equal, and **τροπος**: is the behaviour, so its something that behaves the same way in all directions). 

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**Homogeneity does not necessarily imply isotropy**. For example sheets of metal after being cold rolled have different properties in the direction along the length of the cold rolling, compared to the through thickness. They come from the same material and they have the same density (homogeneous), but the have different properties in the different directions.  

[![enter image description here][1]][1]

**Figure : cold rolled sheets of metal (source: [manufactruing guide](https://www.manufacturingguide.com/en/cold-rolling-sheets) )**


  [1]: https://i.sstatic.net/Bd8VE.png