Different cervical pap smear cell categorization schemes have recently been presented, the majority of which were binary classifications of normal and abnormal cells. This paper presents the findings of a comprehensive investigation on machine learning and deep learning algorithms for binary and multi-class classification on pap smear images from the Herlev dataset. There are 917 photos in this collection, divided into seven normal and pathological categories. The Google Colab platform was used to generate models utilizing all of the techniques using scikit learn and the keras library from TensorFlow. To begin, several repetitions of processes such as feature importance selection, data normalization, standardization, PCA, T-SNE, and others have been imposed on models such as SVM and XGBoost in this work for machine learning approaches. Second, it was demonstrated in this work that a transfer learning-based CNN model from deep learning can outperform machine learning models in terms of binary and multi-class classifications. Furthermore, it was discovered in this work how computationally time efficient it is to apply a transfer learning model, which required roughly 25 min for 100 epochs. Finally, with several iterations of processes and outcomes, this work demonstrates that given enough data for a multi-class pap smear image classification system, the transfer learning CNN model has a higher potential to get the best results than the machine learning models used.