Alzheimer’s disease and schizophrenia are among the most common and complex neuropsychiatric disorders, and their differential diagnosis, particularly in the early stages, poses significant challenges. Although current diagnostic methods provide valuable information, they are often costly and, in some cases, invasive. In this study, a non-invasive and cost-effective approach based on EEG signals and machine learning algorithms is proposed to differentiate between these two disorders. In the proposed method, EEG signals are first decomposed into various frequency sub-bands using the Fast Fourier Transform (FFT), and a set of statistical and nonlinear features, including kurtosis, skewness, Shannon entropy, fuzzy entropy, mobility, and complexity, are extracted. Feature selection is performed using the ReliefF algorithm, and the selected features are subsequently fed into classifiers such as k-nearest neighbors, linear support vector machine, random forest, and others. The performance of the proposed method was initially evaluated on the first dataset, which consists of two distinct parts containing data from patients with Alzheimer’s disease and schizophrenia, where the random forest (RF) classifier achieved the best performance with an average accuracy of 98.61%. Furthermore, evaluation on the second dataset showed that the proposed method, using the same classifier, achieved an average accuracy of 88.11%, confirming the strong capability of the model in distinguishing between patients with Alzheimer’s disease and schizophrenia. It is worth noting that fuzzy entropy consistently outperformed other features across both datasets and was identified as a key indicator in the differentiation of these two disorders.