In US English, there is no effective difference. The sentences that use the definite article are still not talking about a truly specific item since the indefinite article preceding the source negates any particularity.
In US usage the ... a ... is probably more frequent than a ... a ..., perhaps to help the listener focus on the part being described, or perhaps simply to avoid repetition.
Note that the examples given all talk about hypotheticals. They do not refer to a particular branch, tree, roof or car. While the ... a ... seems to be more definite than a ... a ..., the second indefinite article keeps the discussion hypothetical.
If the construction were changed to have only one article, it would have to be indefinite to preserve the hypothetical form.
A car roof is made of many different materials
A tree branch will make decent firewood
The car roof is made of many different materials
The tree branch will make decent firewood
The latter two describe a particular roof and branch, not the theoretical roof or branch.
There are times that general reference descriptions use the definite article to describe a single item. In texts or narrations a singular example may stand in for the whole class.
The oak tree is a member of the deciduous group of trees.
This is a rather academic style, and in common speech would seem a bit pedantic.