The federation, which has been using the abbreviation since 1990 and has registered it as a trademark, was concerned that the duplication would be misleading.
The Fundraising Standards Board agreed to remove FSB from all its marketing material and its logo after what it described as a friendly meeting between the two organisations and their lawyers.
"We are having amicable legal discussions with the federation and are working towards an agreement that will not have major financial implications for our members," said a statement from the board.
The new logo agreed with the federation uses the same design as the original, which was unveiled in June 2006 as part of the £250,000 launch of the scheme. The board said it intended "brand awareness by the public" to be a measure of its success.
Stephen Alambritis, head of public affairs for the Federation of Small Businesses, said: "We felt that the Fundraising Standards Board setting themselves up as the FSB would be muddying the picture and that people would be confused.
"To their credit, we have noticed a reduction in the number of times the Fundraising Standards Board is referred to as the FSB in the press, but occasionally there is a story about FSB membership or about FSB recruitment, and people might think it was us."
Alambritis said that a timescale had not been agreed for the change, but added: "They have just launched and set up their website and literature, so we realise that, conceivably, it will take some time to readjust. We understand that all their media and press shots will have to be changed."
He emphasised that the meeting had not been intended as a threat, but confirmed that if a solution had not been reached the federation would have taken legal action.