The concepts are very similar but there are a few differences.
Firstly, fitness is usually applied to alleles or genotypes, reproductive success to individuals.
Secondly (and partially as a consequence of this), fitness is an average or idealised/expected property across a population; but actual reproductive success per individual is stochastic. Individuals possessing an allele with a relative fitness of "2" will on average have twice as many offpsring as their competitors, all else being equal, but individual reproductive success will vary as a consequence of other factors such as predation, parasitism, starvation etc.
Finally, absolute fitness relates to the proportional representation of a genotype in a population. Reproductive success relates to offspring per individual. For example, in a growing population a genotype could be simultaneously declining in proportion while it is increasing in absolute number, if other genotypes are increasing in number more rapidly.