>It means 100% of the phenotypic variation depends on genes, which is quite different.

More precisely, it usually refers to share of the variation within the specific population being studied. For example, when measuring the heritability of height in a wealthy country, you will get a very high heritability estimate, perhaps 0.8-0.9. When measuring the heritability of height in a global population, you'll get a lower heritability estimate, because a significant fraction of your sample will have had their growth somewhat limited by environmental factors like undernutrition or disease. Conversely, if you're studying a population of clones, the heritability will be zero, because there's no genetic variation and all variation must be due to environment.

None of these estimates is more correct than the other, because heritability can only be defined for specific populations with specific distributions of genetic and environmental factors. There is no "ideal heritability."