People can change their IQ to some degree by their environment but only by a few points. Science has proven that the majority of our IQ is simply hereditary.
Curiosity gives someone knowledge because they ask a lot of questions, but intelligence is not based on knowledge. Intelligence is referring to someone's ability to learn. This is based on factors like learning ability, memory and attention span.
Some individuals are born with more intellectual propensity than others. Curiosity also plays a part, but they aren't mutually exclusive. You can be an intelligent, curious person born with intellectual propensities. With that being said, probably our innate intelligence holds more predictive power of intelligence vs. Curiosity alone if they are mutually exclusive.
It's your level of curiosity. Someone who's not interested in being educated on a topic won't remember the information was well as someone who really wanted to learn about it. We're all (for the most part) given equal chances for education, yet some children fail. More often then not the smart people are the curious people, who want to learn.
My parents, now drug addicts, are very unintelligent. I, however, along with my siblings, have a 4.0 GPA. This was due to my curiosity, not heredity. I like to figure out how things can fit together and make life. I am very engaged in science, for this matter. My family history is absolutely unintelligent. Due to my life experience and the people I know, it has brought to my attention, that I couldn't have been near as smart if my curiosity didn't engage.