There is a growing body of work that leverages features extracted viatopological data analysis to train machine learning models. While this field,sometimes known as topological machine learning (TML), has seen some notablesuccesses, an understanding of how the process of learning from topologicalfeatures differs from the process of learning from raw data is still limited.In this work, we begin to address one component of this larger issue by askingwhether a model trained with topological features learns internalrepresentations of data that are fundamentally different than those learned bya model trained with the original raw data. To quantify ``different'', weexploit two popular metrics that can be used to measure the similarity of thehidden representations of data within neural networks, neural stitching andcentered kernel alignment. From these we draw a range of conclusions about howtraining with topological features does and does not change the representationsthat a model learns. Perhaps unsurprisingly, we find that structurally, thehidden representations of models trained and evaluated on topological featuresdiffer substantially compared to those trained and evaluated on thecorresponding raw data. On the other hand, our experiments show that in somecases, these representations can be reconciled (at least to the degree requiredto solve the corresponding task) using a simple affine transformation. Weconjecture that this means that neural networks trained on raw data may extractsome limited topological features in the process of making predictions.