It's all about the chords....
If I play C Ioanian or A Aeolian without a chord behind it, they sound exactly the same. They have the same notes, CDEFGAB.
Without a chord behind it, they may or may not sound different depending on how it's done.
However, if I play a Cmajor under it it will sound Happy, if I play an A Minor under it it will sound sad.
This is true. Providing that it's a Cmaj chord all alone and by itself, or an Am chord all alone and by itself.
In other words, the chords are what make the modes sound different, not the solo notes.
Pretty close. It's the tonal center or central pitch or key note (or in other words "the mode's root note" as the central focal point of the music) that does it.
It would have been better to say that if you played C Ionian or A Aeolian over a C Major chord, then they would both sound the same and that they would both sound like C Ionian. But if you played them both over an Am chord then they'd both sound like A Aeolian.
But it's true a Cmaj chord all alone and by itself under A Aeolian will sound happy and like the major scale, or an Am chord all alone and by itself under C Ionian will sound sad like the minor scale. Because that's what they would be with the mode's root being held down as the "fixed" pitch. The mode's root is then heard as the tonal center or central pitch of the music, and becomes the clear focal point of the music. Thus strongly helping to convey that mode's unique sound.
I'm not nit-picking, I knew what you meant.
I'm just clarifying it for anyone who may be confused.