They are the same, as Kenny Wong says, but there is a difference in use between "have" as an auxiliary and "have" as a possessive verb.
When "have" is an auxiliary verb, both dialects use the contraction, especially in speech. "I have been to store" and "I've been to the store" are both correct. You almost always use the contracted form in speech. I see them both in writing. "I have" is probably preferable in formal writing.
When "have" is the possessive verb, "I have a book", North American English NEVER contracts the "have". I think only "grammatical" verbs (auxiliaries and modals) are contracted, as a rule (and negative endings).
My impression is that this possessive "have" CAN be contracted in UK English, at least in speech: "I've three pounds". But I could be wrong about UK English: I hope someone who speaks UK English will comment on this.