There is no conflict between these two options -- you are creating a false dichotomy out of a continuum.
It might pay off to look at an analogy. Is a definition what the community of language speakers think a word means, or is it what an individual thinks a word means?
Clearly it is both. The range of usable definitions is determined communally, but the particular idiosyncratic usage of a given individual is some point in that range. (To the degree it is correct enough to be usable.)
We select our values, or our definitions out of a collection of socially determined options. If we simply invented them out of nothing, they would not be values, or definitions. They would simply be choices without any of the power that definitions or values have.
When someone develops a habit of using some given noise to express an emotion or to mumble while ruminating, purely for his own use, he has not given a word a definition, he has only developed a habit for himself. Likewise when a baby cries because it wants a toy, we do not consider this the expression of a value, only of a desire. The love of pizza is a taste, not a value.
At the same time our exact understanding of a definition or a value is still particularly ours, since we cannot share the contents of our mind.