Are these two terms "prototype" and "centroid" exchangeable? I know prototypes can be calculated using the mean of the features. Is it the same for centroid?
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No, they are not exchangeable.
Centroid refers to "the arithmetic mean position of all the points in the figure". Sometimes, it does not make sense to take the mean of the data feature vectors. For instance, when clustering time series, normally you cannot apply the k-Means algorithm because it computes the cluster prototypes with the arithmetic mean; instead, for time series you may use the k-medoids algorithm, which uses actual data points as cluster prototypes.
