Thomas,
Your explanation is correct and helpful! I never thought about the issue of how the rhythmic grid sometimes aligns with notes therefore giving an impression of things being moved to the next note rather than grid! (In some cases these are the same!). (Your assumption that my grid and written notes were of the same value was correct!)
Thanks again for your insight!
Marc,
The only time I get a “beep” is when I use the Control key in conjunction with command or option. Perhaps your system or computer behaves differently than mine. I can confirm that alt+cmd+arrow does move things by a grid step, while alt+arrow moves things to the next or previous note.
[EDITED original post to show “SOLVED”]