The lens-makers formula is actually a more general form of the lens
formula. It can be applied to meniscus lens. In the formula, (N-1) only
represent the differences between the refrctive index and one, which
I THINK with no special meanings.
The lens formula, is a simplied formula and cannot be applied to
meniscus lens. It is generally used to calculate the biconcave (or
biconvex) lens.
As for the meniscus lens, it is a lens with two curved surfaces.
The picture of different lens can be read on:
http://en.wikipedia.org/wiki/Lens_(optics)#Lensmaker.27s_equation