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Will an error on one credit report change my entire score?

Today I discovered that there are 2 accounts that are in very bad condition on my TransUnion credit report. These accounts are not mine and actually occurred when I was a toddler. I called TransUnion to dispute the accounts and checked Experian and Equifax, but the error was not on these two reports. When this is removed from my TransUnion report will my credit report improve as a whole or is there a seperate FICO score for each credit reporting agency and it will only improve a TransUnion score?
Also, the man at Transunion said it takes about 30 days to settle a dispute. Does that mean that my score will change in 30 days as well or does it take a longer period of time to change the score after it is removed?

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