Got versus Gotten and Got versus Have
Got versus Gotten
The word gotten is rarely used in the United Kingdom. In the United States, it is the more popular choice as the past participle of get, but either got or gotten is acceptable.
UK - I will get the file for you. I have got the file for you.
US - I will get the file for you. I have gotten the file for you.
UK - My work will get better as I get more experience. My work has got better.
US - My work will get better as I get more experience. My work has gotten better.
Got versus Have
The words got and gotten are often used for emphasis. They imply more action rather than that implied by using the word have by itself: “I've got the answer" or "I’ve gotten the answer” emphasizes that action was taken -- that work was done. Here, the words got and gotten are not equivalent to the word have which just shows possession.
Also, many speakers in both the United Kingdom and the United States use the word got to express urgency. While the usage may seem redundant, the expressions actually are grammatically correct.
"I've got to go!" (Equally correct - "I must go!" "I have to go!" "I need to go!")