Without knowing the context, in general, "have got" is more colloquial/informal and something that we would say rather than something we would write. It also tends to be a more British way of phrasing (although we do it in the US too). It's also sometimes used for emphasis. For example: I have a cold. - Good grammar, proper written form (always correct). I have got a cold. / I've got a cold - We understand that it means the same as above, but more colloquial/spoken. I have to go. - Again, always correct. I have got to go. Connotation: I have to go *right now.*

By and large, they mean the same thing. "I have" may come across as a little more academic, though. Technically, since the verb "have" is in the present tense and the verb "have got" is in the present perfect (the present perfect is used to indicate that an action started in the past and is continuing in the present, whereas the present tense is used to limit the action to the present, often indicating a habit), we could maintain that "have got" stresses the idea that you started "having" some time in the past.

"Have got" is correct British English. You occasionally hear "Have got" spoken in the USA but here it comes across as redundant at best, uneducated at worst. The reason why you don't see "Have got" that much on the Internet is that American English is more predominant on the Internet than British English.

i have got or i have are same meanings , but '' i were" is incorrect

I guess it is because we're taught British English, not American English.