I am trying to understand Variations, adaptations and selective advantages and how they are all related. Feel free to add or correct me if I'm wrong- Variations are structural, functional, or physiological differences between individual's within a species that result from mutations. If the variation provides a selective advantage (genetic advantage) the organism's chances of survival in terms of both survival in a changing environment and reproduction increases. The variation is then considered an adaptation. So basically adaptations are variations which provide a genetic advantage and give some organisms within a species a better chance of survival than those without the adaptations. This survival advantage allows those organisms to reproduce and pass on their adaptation more frequently than those who do not possess these adaptations.
I would define variation as something a little less specific. When talking about evolution I would consider it to mean any phenotypic variation that exists. I say phenotype because that is what selection "sees" but there can be genetic variation without phenotypic variation (see synonymous mutations). The trait could be physiological, morphological, behavioral or a life history trait (a trait which, all else remaining constant, affects fitness e.g. Lifespan or development time). This is also not necessarily just within species too, comparing homologous trait between two species could reveal between-species variation. For example, in one species every individual might day at exactly 100 days old, in another it may be 102 days, there is no variance within species but there is variance between. The phenotypic variation can be a result of genotype, environment, or a genotype-environment interaction.
If a trait positively affects fitness it is an adaptation, it is a trait that offers some kind of benefit over other current or previous incarnations of the trait. The variance for that trait can be zero - a highly adaptive trait is likely to spread rapidly and variation for that trait would zero if it was entirely genetically defined and fixed in the population but that trait would still be considered an adaptation. I would define fitness as the lifetime reproductive success of your evolutionary unit, commonly thought to be the gene. If a variant of a trait increases relative fitness it provides a selective advantage, and any genes (alleles) causing that trait should spread through the population at the expense of other alleles.
It is important to remember that not every biologist will define these in the same way, there is some debate about definitions in biology.