"They will have problems with the budget."
Translation:Вони будуть мати проблеми з бюджетом.
No, there's no difference in meaning. It's just another way to form Future in Ukrainian
From that link:
The two imperfective future formations may be termed "analytic" and "synthetic"; the former means that it is formed by using discrete words (much as in English "I shall + verb X"), while the latter refers to the expression of futurity by the means of an ending ("verb X-ending")
The analytic future consists of the non-past of бути which has future meaning, together with the infinitive of the imperfective verb
1 sg буду читати
2 sg будеш читати
3 sg буде читати
1 pl будемо читати
2 pl будете читати
3 pl будуть читати
The synthetic future is constructed be means of the imperfective infinitive + personal endings: му, меш, ме, мемо, мете, муть
1 sg читатиму
2 sg читатимеш
3 sg читатиме
1 pl читатимемо
2 pl читатимете
3 pl читатимуть
There is no functional or semantic difference between the two future formations; the synthetic tends to be used less frequently than the analytic, especially in Western Ukraine.
That is fascinating, especially if it is found more in Eastern Ukraine than Western, since as far as I know, there is nothing like this in Russian. I had not seen anything like it in Czech or Slovak either, but I thought maybe it was a Western thing that one would find in Polish. Of course, I guess it really does look to me a bit like the Russian verb for to have (иметь) tacked onto the end of the verb. What a fascinating Ukrainian form. Thank you very much for explaining it to me.