The increasing use of sensors in machine tools and production contexts creates a growing pool of applications for the analysis of time series data. Algorithmic advances have made it possible to consider shape-based representations of time series as a viable alternative to purely feature-based representations for the analysis. From an engineers perspective, a handful of characteristic shapes can be more useful for the intuitive understanding and explainability of real-world phenomena than an entangled set of abstract features. Therefore, a novel approach is presented on how time series snippets (a matrix profile-based motif identification algorithm) can be used for this purpose. In order to succeed not only in the scientific field, the approach must meet the practical requirements of engineers. The proposed method is accessible and can be configured with only few parameters. The method is validated on a dataset from the field of milling. In summary, process fingerprints are computed from shapes that outperform or keep pace with conventional feature-based representations in clustering operations and as part of data-driven condition monitoring pipelines. The fact that a time series segmentation is obtained as a by-product is valuable for practical applications. Having a resulting set of characteristic motifs opens up new ways to utilize Explainable Artificial Intelligence (XAI), which in turn motivates further application studies in this direction.