Yes:
• Next means the one that comes after, like a train, a show, an act in a play, a step in a process, an opportunity;
• Following refers to the next one after a specific time, place or physical marker: "We arrived on the 3pm train, and my brother arrived on the following train." [the train after the 3pm train specifically]. "Her father came from the war in 1963 and died the following year." [the year after 1963].
• Following also introduces text or speech or a list: "Read the following paragraph" "Answer the following questions" "He told me the following: ... " "Please read the following books: ..."
• Subsequent means the one or the ones that follow or result from something: "You should study my response and all subsequent responses from native speakers." [= all the responses that follow mine]