One widely used application of artificial intelligence (AI) in today's globalized world is machine translation (MT). Studies show a growing need for an understanding of how to use MT critically, or MT literacy, amongst not only translation and language students but all users. Given the current interest in using generative large language models (LLM) for translation-related tasks, the question arises to what extent MT literacy now also entails knowing how LLMs and generative AI (GenAI) work. Our paper explores how university students enrolled in translation, language and AI courses in Finland, Belgium and the Netherlands understand how MT works and what its defining characteristics are as compared to human translation (HT). We find that, overall, students consider MT distinct from HT, although many also perceive important similarities. However, some of these similarities are based on misconceptions and a tendency to humanize the technology. We argue for a need to (re)define more clearly what MT Literacy entails to empower both professional and informal users to use GenAI for translation effectively and critically.