What is the difference between the following sentences:
Мой папа в командировке.
У меня папа в командировке.
How can I explain to foreign students when to use "мой" or "у меня"?
Well, the first thing that kind of stands out to me is that 'у меня' can mean 'I have', while 'мой' would not convey that meaning on its own. For example:
This statement sounds complete. It reports the fact of the existence of some conflict between the speaker and his boss in the present time.
This statement is incomplete. It doesn't report any message. In fact, it doesn't report anything. It only names a certain phenomenon - a conflict of a speaker with his boss - however, we know nothing about it. We don't know whether this conflict has started, is still going on or is already over. We know nothing about how big this conflict was (is, has been, or will be). We don't even know whether it is really a phenomenon (something having its place in the objective reality) or simply a concept in the speaker's mind (like in "Иногда пытаюсь представить себе, каким бы мог быть мой конфликт с моим начальником, если бы он мог произойти").
Another difference that comes to my mind is that 'мой' cannot modify a personal pronoun, while 'у меня' can. For example:
(Not 'Он мой ещё маленький'!)
The same is true about possessive adjectives ('мамин', 'папин', 'сестрин', 'дедушкин', etc.). For example:
(Not 'Я мамин – вместо швабры')
Also, 'у меня' can simply mean 'at my house', in which case it may not at all mean 'мой'. For example:
(Not 'Твой друг уже мой', which could meаn a totally different thing :) )
One more thing, 'у меня', 'у тебя', 'у ниx' and so on, can mean 'in my/your/their thinking' or 'in my/your/their understanding' or 'in my/your/their own little world', in other words, can describe how someone treats something else or somebody else. In this case it does not describe possession at all. For example, compare:
In the first sentence the speaker is stating the fact that the consultants are ignorant, while in the second sentence he seems to be even defending consultants. In the first sentence consultants belong to the one to whom the speaker is talking, while in the second sentence the person to whom the speaker is talking (interlocutor) may not have, i.e. possess, any consultants at all (in the first sentence, the speaker is talking only about those consultants that belong to his interlocutor, while in the second sentence he is talking about all consultants).
Finally, 'у меня', can describe a certain situation that the speaker has or is experiencing at the moment, while using 'мой' would not have such a connotation. Compare the following examples:
In the second example, the speaker is introducing and describing her particular situation that she is presenting as a reason why she cannot go hiking. In the first example, however, the fact that the speaker's father is on the business trip is not being presented or described as a particular situation.
My answer reflects only my limited understanding of the matter and in no way should be taken as a comprehensive description of it.
There is no difference in the meaning of the two sentences:
In both cases, the meaning is that my dad is away on business.
There is, however, a slight difference in focus between the two. In the first case, the main focus of the sentence is папа - he is away on business; oh, and he happened to be my dad.
In the second sentence, words у меня shift the focus onto myself: I have this dad, who happened to be away on business:
The best English analogues of the two sentences I can think of are (respectively):
In this particular case, there is actually no difference how to say it:
В данном случае речь идёт о конкретной (единственной) маме.
Мама чья? Его (и только его).
У кого есть мама? У неё (и только у неё).
One more example:
Опять же, речь о конкретной собаке.
Собака чья? Их (и только их).
У кого есть собака? У них (и только у них).
И снова - конкретный брат.
Брат чей? Ильи (и только Ильи).
У кого есть брат? У Ильи (и только у Ильи).
Generally, where you can use "мой", you can use "у меня" as well.
У кого нет денег? У меня.
In case of negation, sometimes you can't change phrase.
This is a very interesting question. Thanks Olga!
While the construction "Мой папа ..." has a direct corresponding translation into English to "My father...", the second one is more specific to Russian.
The question slightly "blurred" by the fact that in both Russian phrases the verb is missing and understood. It would be the English verb is. The meaning of the two phrases is also very similar. Apart from that grammatically phrases are very different.
The first phrase is a simple (usual) sentence with a subject (my father), a verb (is), and the rest. The second phrase is an impersonal construction. The most direct correspondence to this in English will be "It is ..." or "There is ..." constructions.
Moreover (similar Russian construction in dative case):
And finally, one more (and probably the biggest) complication is that "у меня", "у нас", "у них" does not have a direct correspondence in English. The direct meaning correspondence would be "in my(our,their) world" (including both internal and external worlds). Or in other words: "In my current circumstances." Of course you will not translate it like this literally. Every time you will need to invent something more suitable for English like "there is no money in my possession". Or just flip the phrase into ordinary sentence with personal subject, if other translations are completely ugly.
So in conclusion: It is just a coincidence that
The first one conveys the meaning that there is only one father (the father) while the second does not convey such meaning.
Since people typically have only one father, the sentences are interchangeable.
But if you said about a dog or about a sister, the sentences would have different meaning.
Моя сестра заболела = My sister is ill (that is the only sister)
У меня сестра заболела = A sister of mine is ill (there can be one or several sisters)
You cannot say "Моя сестра заболела" if you have several sisters and it is not clear about which one you are speaking about.