Parkinson’s disease (PD) and Essential Tremor (ET) are the most common tremor syndromes in the world. Currently, a specific Single Photon Emission Computed Tomography (123I-FP-CIT SPECT) has proven to be an effective tool for the diagnosis of these diseases (97% sensitivity and 100% specificity). However, this test is invasive and expensive, and not all countries can have a SPECT system for an accurate differential diagnosis of PD patients. Clinical evaluation by a neurologist remains the gold standard for PD diagnosis, although the accuracy of this protocol depends on the experience and expertise of the physician. Wearable devices have been found to be a potential tool to help in differential diagnosis of PD and ET in early or complex cases. In this paper, we analyze the linear acceleration of the hand tremor recorded with a built-in accelerometer of a mobile phone, with a sampling frequency of 100 Hz. This hand tremor signal was thoroughly analyzed to extract different kinematic features in the frequency domain. These features were used to explore different Machine Learning methods to automatically classify and differentiate between healthy subjects and hand tremor patients (HETR Group) and, subsequently, patients with PD and ET (ETPD Group). Sensitivity of 90.0% and Specificity of 100.0% were obtained with classifiers of the HETR group. On the other hand, classifiers with Sensitivity ranges from 90.0% to 100.0% and Specificity from 80% to 100% were obtained for the ETPD group. These results indicate that the method proposed can be a potential tool to help the clinicians on differential diagnosis in complex or early hand tremor cases