"running out" implies a change in the situation from having something to not having something. I don't drink milk very often. I have not had any milk in the house for weeks. So I haven't run out of milk, I just don't have any. I did use all of my butter this morning, though, so I ran out of butter. In your daughter's case, any of the sentences would be fine.

Hi Viktoriya All of your example sentences mean the same thing in the context you gave. It is important though to make a quick point about the title of your question - "To be run out of smth. / to be out of smth. / etc." - but in fact you have not constructed any sentences with "To be run out of something". There are 3 phrases you need to think about: 1 . To BE RUN OUT of something = to be forced to leave "To be run out of town." 2. To BE OUT of something = To have no more of something and 3. To RUN OUT of something = To finish your supply of something. Therefore 2 and 3 mean almost the same thing (just like your examples), but number 1 is something completely different. I hope this explanation makes sense. Chris

If we take the situation you suggested I think I've run out of milk is fine. This tends to be used referring to the moment you have none left, I'm out of milk is more likely to be something you say to yourself while writing a shopping list. In other words you used the last of the milk some time earlier.

Yes, they all mean the same thing. As a native British-English speaker (2) sounds slightly more American to me, but apart from that they are equivalent.