My basic ideas about intelligence, genetic endowment and childhood environment, based on absolutely no scientific research whatsoever -
I have doubts that there can be one single definition of 'intelligence' that covers all the common uses of the concept. The closest I think we can come to one that is general enough yet still contentful is to define it as a basic capacity to learn, to adsorb information and make use of it, probably with some reference to the speed of this process. It would make sense if this capacity was at least partially genetically inherited, and related at base to properties of the brain.
There is a potential argument that this basic skill will always come bundled with some innate specification to a domain - we see this in our talk of people having more practical or more theoretical minds, more artisic or more scientific minds, etc. I am genuinely unsure about the evidence for or against this claim.
What is clear, however, is that whether or not intelligence is innately tied to an object, the environment a child grows up in, which will include the influence of family, wider community and education, will to some extent limit and direct their intelligence towards certain objects, some of which will happen to be favoured by society and the economy at certain times, some of which will not. It is in this way that a gap between intelligence and success can arise.