I would disagree: in English, to wish and to want are not the same thing; they are very similar in meaning and frequently interchangeable, but there is a distinction. In French, the same thing is true: vouloir and souhaiter have very similar meanings, but roughly the same distinction exists between them. It is therefore right that Duolingo should teach us that vouloir means to want, while souhaiter means to wish.
There are other similar ways to express this feeling, but they too have nuanced differences (of strength or kind of feeling, or register of expression). There are two ways one can learn these nuances: by correspondence with equivalent English words, or by contextualisation. As you note, Duolingo does not provide the latter, so it must rely on the former.
- I want to help
- I wish to help
- I desire to help
- I would like help
- I crave to help
- I hope to help
- I intend to help
- I aspire to help
And their French equivalents (some of which are rougher than others)
- Je veux aider
- Je souhaite aider
- Je désire aider
- Je voudrais aider/j'aimerais aider
- J'appète aider (very rarely used - probably better expressed as "désirer avidemment" or similar)
- J'espère aider
- J'ai l'intention d'aider
- J'aspire à aider
I agree as a linguistic matter. I also initially translated it as "I would like to have a son" because that's the first English construction that popped into my head. I don't believe "to wish to (do something)" is as common in English as want to/would like to.
But, that said, I don't expect a tool like this to accept every subtly different verb in the want/hope/wish/desire/like family as interchangeable. I just started reviewing French on here yesterday, and I often forget to use the most literal word-for-word translations as lemmingofdestiny has paired them up. But I try to remember.
Hope is "espérer". I suppose the distinction between hoping and wishing is a nuanced one, but as a native English speaker, I would say you hope for things you want to believe are possible, or that you expect may happen. Wishing expresses a stronger, more immediate desire, but one that is not necessarily tied to expectation of reality. E.g. "I wish I were taller right now, even though I'm an adult and know I will never grow again." versus "I hope I will be taller when I grower up."
I suppose I broadly agree, but the translation of this very sentence, "I wish for a son", shows that "wish" can also be used for realistic things (if it were unrealistic, one would say "I would I could have a son"). In any case, "I am hoping to have a son" is accepted as correct now.
"I wish to have a son" was not accepted, though this is what a prospective parent might say. "I wish for" and "I wish to have" mean the same thing, especially when it concerns a physical being. For example, one would say "I wish to have a son/daughter/friend/etc.," but "I wish for wisdom".