I fundamentally disagree that this distinction exists, and even if it did this is not a situation where it would apply.
But it does exist; preaching is persuading or guiding others to follow your own beliefs. If no distinction existed then we would be mechanically bound to preach what we believe, and we’re not, so it’s a choice.
Everyone is a hypocrite to some degree. There are levels of hypocrisy that are breathtaking, and levels that are just meh.
‘Thou shalt not kill’ is a biblical commandment, not a principle. It comes from the fundamental principle of harm minimisation, and the two examples you gave are different (extreme) applications of that principle, see: the trolley problem etc. It’s morality for babies; looking at extreme black and white cases to be able to get a clear, consensus issue. Life is rarely that simple. Morality is never that simple.
They straight up went “when I break my own moral principles it doesn’t feel as bad as when others break them against me”
I’m not sure, that seems like another extreme interpretation of something more nuanced.