Is IQ the same as intelligence?
Intelligence and IQ are not the same thing. Your IQ is a measurement (a number) of the 'intelligence' trait that each and everyone has to a greater or lesser degree in comparison with others.
It is remarkable that measurements of the IQ preceded discussions on what the concept of intelligence actually entailed. Usually this would be the other way around, first the concept and then the measurements. Looking at the history of the IQ test concept and the way it was used (and abused), clarifies the development described above.
Origins of the IQ
By the end of the 19th century it was assumed that everybody had the same abilities and that people only differed in their effort level and heritage. Charles Darwin overturned that assumption by suggesting variations as the driving force behind natural selection and evolution.
Galton, a cousin of Darwin, found this assumption reflected in the exam results of first-year students at Cambridge university. Grades for mathematics exams varied greatly between students and Galton argued these variations were related to differences in (hereditary) intellectual abilities (intelligence). In essence these exam results, just as contemporary school performance measurements, were a measure of intelligence (almost the same as IQ scores).
Use and abuse of IQ and intelligence measurements
Intelligence measurements were initially intended to measure individual differences. Up until today, the move to the next school grade and the choice of school are determined in this way, even though they are not based on actual IQ test scores. There is nothing wrong with this use of intelligence measurements, such as 'IQ', but measuring the individual differences has also opened up the possibility of a less positive use.
Thus over time IQ tests have been used to preserve social differences, or for example to have immigrants be returned to their country of origin based on low intelligence. Also, IQ tests have contributed to the inception of the eugenics movement.
The Q of 'quotient'
The IQ as a measurement of intelligence is a relative measurement. You do not have a fixed IQ (as you do have a specific weight and body length), but your IQ indicates how well you are doing in comparison to others. Compared with 50 Einsteins you would have a very low IQ, compared with 50 children in the second grade you would have a much higher IQ.
Your IQ therefore is a score you achieve relative to a group of others. The average of that group is defined as 100. That is why we call it a 'quotient'. And that is why IQ is not the same thing as intelligence.