"Today is Thursday."
Translation:Dziś jest czwartek.
I'd like to hear that too, but my working hypothesis until then is that czwartek is the subject of the sentence, because dziś is an adverb and therefore can't be the subject.
like someone already answered there is no difference, other than other than the fact that one is a syllable longer than other, and that makes one sound better in some sentences and other in different sentences. (Dzisiaj is better than dziś at the end of sentence).
It is incorrect. You can only use the 'to' construction if there are noun phrases on both sides.
"dziś" is an adverb.
Besides, this "to" can be interpreted as "=" sign. In this way you are saying that "Today = Thursday". And it's not exactly true, because the meaning of 'today' changes every day.