Yes, and no. It is hard to answer this, because of the variety of ways Baptists describe themselves, both officially or unofficially. For example, our church is independent in the sense that we are not affiliated with any association, convention, or fellowship. It is not part of our official name, though we do (with caution) tell people we are independent Baptists. Most people around here are apt to identify "independent Baptist" with the Baptist Bible Fellowship, who were the first people in the area to stress it as an identifier. We hold the fundamentals of the faith and would be considered Fundamentalists by a lot of folks, but we don't identify ourselves by the terminology Fundamental Baptists.
Some who use Independent Baptist -- as opposed to Independent Fundamental Baptist -- may be trying to distant themselves from Fundamentalists, but most Independent Baptists are Fundamentalists or nearly so (according to how you define Fundamentalist).
I know a pastor who says if the local tv station calls him and asks if he's a Fundamentalist, he'd say no. Why because he is not their definition of a fundamentalist.
In the run-up to the centennial anniversary of the founding of the Fundamentalist Fellowship of the Northern Baptist Convention, the now-independent splinter successor group has rebranded as 'Foundations' Baptist Fellowship International.
I don't think they're fooling anybody.
They aren't trying to "fool anyone." Have you read Kevin Schaal's
Why Change To Foundations at ProclaimandDefend.org? Further, the FBFI is not a "splinter successor group." It is a direct lineal descendant of the FBFNBC.