'I have two brothers' and 'I've got two brothers' have exactly the same meaning. The only difference is that the 'I've got' version is slightly more informal. BUT..... 'I have' and 'I've got' are interchangeable ONLY in the following situations: 1. When the verb 'have' is the main verb, referring to possession or something/someone that is 'yours'. You can't use 'I've got' as an alternative when 'have' has another meaning - for example, 'We always have breakfast at 7 am'. It is not possible to use the 'got' form in this situation. Nor can you use it when 'have' is an auxiliary verb - for example, 'I have seen that film'. 2. In the present simple tense. There is no equivalent of 'I've got' as an alternative to 'I have' in other tenses. For example, the past of 'I've got a problem' is 'I had a problem' and the future is 'I'll have a problem'. 'Got' can't be used in this way in other tenses. 3. In formal contexts. It is fine to use 'I've got ..' in spoken English, and for most informal and neutral written contexts, but would not be appropriate for an academic essay or legal document, for example. NB It is also very important not to confuse this idiomatic use of the word 'got' with the normal use of the verb 'to get', meaning obtain, receive, arrive, become and so on. I hope this helps. This question has been asked hundreds of times on italki, and I've answered it many many times myself. Please ask if anything isn't clear.

I'll do my best to answer your question as thoroughly as possible. "I've got" literally means "I have got," which does not seem like proper English, but we use it colloquially when speaking to each other: "I've got a cool car; I've got to go, etc." I would say it generally means the same thing as "I have." The difference, if any, is simply with what the two phrases imply when you use "gotten." "I've got a cool car," means the same as "I have a cool car," but it is a bit more slang to say "I've got." However, if you say "I've just gotten a cool car," it means "I have just received a cool car," which is a bit different. I would say in general, the two are the same, and from a language learner's perspective, they are completely the same, but again "I've got" is more informal, colloquial, and possibly improper (not quite sure but I'd use both in everyday conversation). Hope this helps!

I'm sure if I thought hard enough I could think of an example of when they have a difference in meaning. But I can't think of one easily. I have 10 shoes. == I've got 10 shoes. I have to run. == I've got to run. It doesn't really make a difference. "I've got" is a bit less...formal.