On paper it is the same scale starting on different notes but what humans hear is different flavors that modes offer. A aeolian and C ionian have all the same chords and notes they just start at a different location and thus sound way different to the human ear. Whenever you change the tonic on the scale your building the melody over you need to change the order of chords that are supporting that melody also and that's what people forget.
I can translate what you just said to "major key songs sound different from minor key songs" except I used a lot fewer words to say it, and my students are less confused than your students.