In the spoken language both forms are used and both forms means "I am" or "They are". Sînt is written according to the old writing norm and I don't think, that it's used in modern texts. According to the new rules it should be written sânt, because î is used only in the beginning and in the end of words and â elswehere, but I haven't encountered such a form.

What I have been told by a Romanian native speaker is that sînt is the archaic version for sunt. So you can say both Eu sunt as Eu sînt and it means exactly the same, just that the last one is the old form.

They are spelling variations of the same word. The old spelling rules (before the 90s) specified that the verb to be should be conjugated like this: sînt (I am / they are), sînteți ( you are - plural), sîntem (we are). Sometime in the 90s the Romanian Language Academy (I'm not sure of it's official name), changed the rules (it's a more complicated topic), and among the new rules, the verb "to be" became "sunt" (I am/they are). The funny thing is that everyone still pronounces this word as ”sînt” (except news anchors, but they don't have a choice) There are still a lot of people who refuse to adhere to the new spelling. So you'll still occasionally see both forms. On the good side, if someone sends you an email and they write "sînt" you'll know for sure they graduated highschool before the 90's :)

"Sunt" was spoken prior to communism and reintroduced after communism. During communism anyone that used the word was "sunt" was considered uneducated. Failure to use the word "sînt" was a way of identifying people that were resistant to communist ideology.