Translation:We are talking about the budget for next year.
They mean two slightly different things. It's currently October 2013, and if I said the "We are talking about next year's budget" I would mean the budget for calendar year 2014, but if I said "We are talking about the next year's budget" I would mean the budget from now until October 2014. I'm not sure how to make that distinction in Portuguese, though.
I really can't understand those sentences like you do....but I can understand what you mean.
I portuguese, it's very common to say "para o ano que vem" (That's definitely the year of 2014). Para o próximo ano would mean the same thing.
I'm Brazilian native, and I confess I cannot find an easy way to express the other thought. I would have to say more or to do some workarounds, like:
"orçamento para o próximo período de um ano".
"o próximo orçamento de um ano". (Now I understand.....the article changes from year to budget when you write it, but shouldn't the possessive go away in this case? "The next year budget?)
I would probably not avoid the "from today" part. (A partir de hoje).
Hm...I still feel like it needs the possessive, but now you've got me second-guessing myself. I'll admit that I don't often talk about budgets--actually, I never talk about budgets. Maybe another English speaker can weigh in? Bem, a partir de hoje, eu sei falar sobre orçamentos em português. Have I got it? :)
"next year's budget" and "the next year's budget" may have a subtle difference which is often a context setter; if I'm talking about 2015 (today is 18Oct14) I personally will not use "the"; But I will use "the" if my reference point is not now or this year, e.g. if we are talking about the budget for 2017 already and then we move on to talk about that for 2018, then pretty much all English speakers would use "the" without ever thinking about it.
It is definitely ambiguous in English to say 'the next year' but I agree with others that it is different to simply saying 'next year's budget'. As gaih says, it makes most sense in relation to discussing first one year and then the next year. Otherwise, without this preceding discussion I would never say 'the next year's budget' as it would be too unclear but, rather, would say 'we are talking about the budget for the next year' which clearly implies 12 months from the point in time of this discussion.