Is the definition of recursion and iteration in signal processing different from computer science?
In my understanding, the term iteration in DSP is usually used in the mathematical sense, i.e., for describing iterative methods solving certain numerical problems. The power method for computing the largest eigenvalue of a matrix and its corresponding eigenvector is a typical example of such an iterative method used in signal processing.

The term recursion is normally used in the sense of recurrence relation, where a value $y_n$ is generally a function of $n$ and of its values $y_k$, $k&lt;n$:

$$y_n=f(n,y_{n-1},y_{n-2},\ldots)$$

In signal processing applications, such as filtering, the index $n$ is interpreted as a time index. E.g., when implementing a (causal) filter, the current filter output can be computed from the current input and previous input and output values. This is a specific form of a recurrence relation. On the other hand, when talking about iteration, the iteration index is usually not related to time. I think it is this latter point that your professor referred to.