Social construct.

[Objectivist]

I don't think that a tree is a social construct.  Nor is a mountain, a cloud, or anything else that exists in reality apart from human choice.  I think that culture is a social construct in that it is a product of a group or society of people.  

I don't agree with you that definitions are based on "one person communicating to another person vaguely what something is".  I think proper definitions serve a very important function and they are objective, i.e., based on facts and there are rules to defining concepts that derive from the process of concept formation.  A definition names the things a concept subsumes in terms of their essential characteristics.  Essential characteristics are what makes a thing what it is and also distinguish the thing from other things. For instance, man is the rational animal. This definition names the fundamental characteristic that makes man what he is and distinguishes him from other animals.  They need to be precise in order to serve their function, which is to facilitate cognition.  In fact, when someone is using vague definitions, they are probably trying to pull the wool over your eyes.  

Definitions are the carriers of truth.

No, definition is the medium of human cognitive organization.   Whether it is the truth depends what you mean by truth.

I disagree.  Definitions of what?  Concepts are the medium of cognitive organization.  They are how we identify and organize the material brought in by the senses and definition is the final step in that process.   A definition is what unites the many units of a concept into a single unit. A definition is true if it corresponds to reality.  That's what I mean by truth.  If we defined a tree as a species of pachyderm, then that would be a false definition.  

What theory of concepts are you using?