Both these phenomena are termed catalysis, but clear and complete discussion and specification of their similar and distinguishing features would be useful.
That is a very broad question. It would help if you could specify what type of catalysts you are interested in (thermal, photo, electro, what type of reaction, etc).
Both involve elementary steps, but for homogeneous, these are homogeneous species, and for heterogeneous, these are species on a surface.
You need to consider available surface area and catalyst coverage on a surface for heterogeneous catalysis, but for homogeneous catalysis, you need to consider concentrations.
Heterogeneous catalysis can be inhibited by covering up the active sites on the surfaces (such as by adding mercury). Often, an induction period will be observed in "homogeneous" reactions where solids are forming, and then catalysis occurs from heterogeneous species.
In electrocatalysis, you can tell the difference by the nature of the electrochemical response.
If you can give more specifics about what type of homogeneous vs heterogeneous catalysis you are interested in, I can post relevant literature.
Heterogeneous catalysis the phase of catalysts differs from that of the reactants or products. On the other hand homogeneous catalysis the catalyst is soluble forms a homogeneous mixture with the reactants . The common feature in both types of reactions reaction occurs at the surface .The rate depends upon the amount of the reactants and nature of the substrate. Sterically crowded substrates may undergo the reactions less readily in both the cases.
and products and ... the surface.
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