Action recognition models, both unimodal and multimodal, have demonstrated strong generalization in tasks such as zero-shot learning, base-to-novel transfer, and domain adaptation. However, can they effectively transfer high-level motion concepts across diverse contexts, even within similar distributions? For example, can a model recognize the broad action "Pushing" when presented with unknown variations such as "Pushing something from right to left"? To explore this, we introduce a motion transferability framework with three datasets: (1) Syn-TA, a synthetic dataset with 3D object motions; (2) Kinetics400-TA; and (3) Something-Something-v2-TA, both adapted from natural video datasets. We evaluate 13 state-of-the-art models on these benchmarks and observe a significant drop in performance when recognizing high-level actions in novel contexts. Our analysis reveals: 1) Multimodal models struggle more with fine-grained unknown actions than coarse ones; 2) The bias-free Syn-TA proves as challenging as real-world datasets, with models showing greater performance drops in controlled settings; 3) Larger models improve transferability when spatial cues dominate but struggle with intensive temporal reasoning, while reliance on object and background cues hinders generalization. We further explore how disentangling coarse and fine motions can improve recognition in temporally challenging datasets. Our study establishes a crucial benchmark for assessing motion transferability in action recognition.