language stringing together a series of concepts. Concepts are formed by creating a conceptual idea. These ideas are created by choosing concepts which are similar (not the same in some way). The way they are not the same is by leaving out the measurements. Which measurements are left off depends upon the concept. Ex. the concept of wavelengths leaves out the measurements of the wavelengths individually.
Therefore the language is already very imprecise to begin with. Other new concepts are created and defined by previous concepts which will be used to define the new concept.
So language is conceptual by definition. The actual definitions of concepts are the referrents of the concepts. Ex. cat means all cats which have ever lived and all cats which will ever exist. This language then is a translation from existence to a mental re-presentation of existence then is a translation from existential to a mental model. This process is VERY conservative (a compression if you wish). One 3 letter concept can re-present a memory image we have all learned and can therefore convey (? Some meaning) to another person who has learned to duplicate the process. Notice however that we each live separate lives and will have unique representations in our unique memories of which cat we think the concept represents at this moment in time.
If you think of the memory as an operating system for each one of us, then we each have to write that operating system as we live out our lives. They (OS's/minds)then are all different to begin with in an extraordinary number of ways.
So to rephrase your question, there is an illusion (only) of understanding. The question is .... is this useful and if so in what way. In my opinion it is only by a careful and slow dialogue that any real meaning or understanding is EVER transmitted between any two individuals. Maybe this imprecise off the top of my head answer will be a good example of this concept.
This brief does not even consider the slippage between the of the messages between the reader and the writer and the reader.
The concept of context alone took me 5 years to sort out before I came up with how it is established, so that I could begin to understand the problem of how and why languages work at all.