Can someone please explain to me, what the difference between the two words tio and ke is? They both translate as that, but I assume that like the words de and da they are used differently.
Tio is a noun-like word, whereas ke is a conjunction. More specifically, tio translates "that [thing]", and is comparable with other noun-like correlatives (kio "what [thing]", ĉio "everything", nenio "nothing", etc.) and with other indicative correlatives (tia "such/that kind of", tiom "that much", tiam "then/that time"). Ke on the other hand is used to connect dependant clauses, ex. Mi diris ke li iris for for "I said that he went away"
Yasmine's answer is great. The following terms help me.
Tio is a deictic element. That is, it points to something. What thing? "That" thing.
ke on the other hand is a complementizer. It's only function is to initiate a complement clause. See Plena Manlibro de Esperanta Gramatiko §33.2 which reads, "La vorteto ke ne vere montras ian signifon. Ĝi nur montras la komencon de subfrazo, kiu ne havas alian frazenkondukilon. Ke-frazo povas roli en multaj diversaj frazroloj."
In English, "that" happens to serve both functions. In many other languages, a different word is used for each function. Hope this helps.