Recently, generative AIs like ChatGPT have become available to the wide public. These tools can for instance be used by students to generate essays or whole theses. But how does a teacher know whether a text is written by a student or an AI? In our work, we explore traditional and new features to (1) detect text generated by AI from scratch and (2) text rephrased by AI. Since we found that classification is more difficult when the AI has been instructed to create the text in a way that a human would not recognize that it was generated by an AI, we also investigate this more advanced case. For our experiments, we produced a new text corpus covering 10 school topics. Our best systems to classify basic and advanced human-generated/AI-generated texts have F1-scores of over 96%. Our best systems for classifying basic and advanced human-generated/AI-rephrased texts have F1-scores of more than 78%. The systems use a combination of perplexity, semantic, list lookup, error-based, readability, AI feedback, and text vector features. Our results show that the new features substantially help to improve the performance of many classifiers. Our best basic text rephrasing detection system even outperforms GPTZero by 183.8% relative in F1-score.