Short Message Service (SMS) is a mobile messaging tool used by billions of people to communicate via a mobile phone. However, due to the lack of proper message filtering techniques, this form of communication is vulnerable to unwanted and junk messages. This paper compared SMS spam detection approaches based on machine learning methods such as Adaptive Boosting (AdaBoost), Extreme Gradient Boosting (XGBoost), K-Nearest Neighbors (KNN), Decision Tree (DT), Random Forest (RF), Multinominal Naïve Bayes (MNB), Logistic Regression (LR), and Support Vector Machines (SVM) and deep learning methods such as Convolutional Neural Networks (CNNs), Artificial Neural Networks (ANNs), and Long Short Term Memory (LSTM) in terms of f-score, accuracy, recall, precision, and a confusion matrix constructed for each strategy. The study tested two different preprocessing methods on two different Turkish SMS datasets to evaluate the approaches. The aim of this study is to contribute to the issue of spam filtering in Turkey. The results indicate that the highest accuracy values were achieved with Support Vector Machine (99.03%) using the first preprocessing method and Logistic Regression and Random Forest (98.07%) using the second preprocessing method on the BigTurkishSMS dataset, a combination of the two datasets used. As is the case with the majority of machine learning algorithms, the second preprocessing of the data set yielded superior results in deep learning models. The ANN model achieved the highest accuracy, with a score of 97.41%. The study employed a comparison of machine learning and deep learning techniques on Turkish SMS datasets, which will provide valuable insights for researchers working in this field.