Home-based rehabilitation is essential for stroke survivors, facilitating motor recovery and improving activities-of-daily-life performance. Recent advances in wearable technologies and machine learning promise to revolutionize home-based arm rehabilitation by providing detailed movement analysis. However, machine learning algorithms for arm movement identification are predominantly trained and tested in the same environments. Their ability to generalize to novel environments remains largely unknown, hindering practical applications. This paper investigates the ability of two established machine learning models to generalize a structured, lab-based environment to a more realistic, semi-structured kitchen environment. Twelve healthy participants performed various arm activities, involving three arm movement types (reaching, lifting, and pronation/supination). In addition to evaluating the generalization of movement identification, we compared algorithm performance for two different sensor configurations: four Inertial Measurement Units (IMUs) on the arm versus a single IMU on the wrist. We employed a Random Forest (RF) classifier and a hybrid deep learning model combining convolutional and recurrent neural networks, evaluating both subject-specific and group approaches. Trained in the structured environment, the RF classifier predicted activities in the semi-structured environment with 86.54% (subject-specific) and 77.37% (group) balanced accuracy, based on the four-sensor configuration, while the hybrid model reached 87.96% and 82.96% accuracy. The accuracy was lower with a single wrist IMU; the RF classifier showed a smaller decrease than the hybrid model. Our findings demonstrate that the investigated arm movement identification algorithms generalize well across environments even with the minimal sensor configuration, indicating the potential for future applications in home-based stroke rehabilitation.