
the rendering equation can theoretically be described in all known detail, and, as such, isn't at this moment an approximation. it is (till now? :D till ever, i'd guess) not possible to implement it in any way without approximating a.k.a. some discrete sampling routines.
approximations are the things you can not use in the final simulation. a final simulation can not solve the equation, possibly. but you can raise parameters to infinity and at one point, it would theoretically solve the equation.
specular lighting is not part of the equation. it can be used to approximate a similar solution, but it will not solve the equation.
thats where i draw the difference. there are "solutions" to a problem (or part of it). they are, or converge towards the solution of the original requested equation. approximations are things that won't exactly ever solve the equation.
specular lighting is part of the phong equation. but the phong equation is only an approximation for a more complex material with glossy reflection on it.
and, in theory, approximations are useless. in practice, sometimes you don't need the full correct solution, but can get away with a part of it, or a part that is near to it.
rasterising is full of such approximations. bumped enviroment maps will never be 100% correct reflections, but they look close enough to be good enough in most cases. but they are, and will always be, an approximation.
