I cannot stop seeing them very related to each other. In one the product is not explicitly defined (it is said that it is the result of a series of cuts) in the other it is stressed that $\epsilon^2=0$ is the defining property.
Both are related to derivatives when evaluated in functions (for example of polynomials or Taylor series) although in one the
st symbol is used and in the other $\epsilon$ is used.
Is there a simple relation between these two mathematical constructs? are both the same? is one just a specialization (for a certain operation) case of the other? Is one a field and the other just a ring for example? Is the difference the partial vs. total order?