In Ensemble Stars!! Basic, Appeal Talks are randomized conversation events the player receives when playing any kind of produce course, such as event or D.L.F.S. courses. Each character has 3 Appeal Talks total. To potentially trigger an appeal talk of a particular character during a course, you must click on a room that contains the character in it.
Minitalks are the conversation events a player receives when playing any kind of produce course that contains a companion character, such as event or D.L.F.S. courses. Each companion character has 6 Minitalks total; 3 normal, and 3 special. To trigger any minitalk, you must complete the criteria stated in the upper left corner of the course screen, located next to the turn counter.