Thyroid cancer is the most common type of endocrine cancer. Most cases are called differentiated thyroid cancer (DTC), which includes papillary, follicular, and Hurthle cell types. DTC usually grows slowly and has a good prognosis, especially when found early and treated with surgery, radioactive iodine, and thyroid hormone therapy. However, cancer can come back sometimes even years after treatment. This recurrence can appear as abnormal blood tests or as lumps in the neck or other parts of the body. Being able to predict and detect these recurrences early is important for improving patient care and planning follow-up treatment. In this view, this research explores the different machine learning algorithms and neural networks to effectively predict DTC recurrence. A total of 16 machine learning algorithms were utilized for the experiment, namely, logistic regression, random forest, k-nearest neighbors, Gaussian naïve Bayes, multi-layered perceptron, extreme gradient boosting, adaptive boosting, gradient boosting classifier, extra tree classifier (ETC), light gradient boosting machine, categorical boosting, Bernoulli naïve Bayes, complement naïve Bayes, multinomial naïve Bayes, histogram-based gradient boosting, and nearest centroid, followed by building an artificial neural network. Among the classifiers, ETC performed best with 98.7% accuracy, 99.99% precision, 95.45% recall, 99.99% specificity, 97.67% F1 score, and 99.5% AUROC. To improve model interpretability, Shapley Additive Explanations (SHAP) was also used to explain the contribution of each clinical feature to the model's predictions, allowing for transparent, patient-specific insights into which factors were most important for predicting recurrence, thereby supporting the proposed model’s clinical relevance.