"Why not use terminology which is clear so that the rest of the world can understand it?"
What, and have the rest of the world see the emperor naked?
"Outside of the art world, people try to use words in order to convey meaning as clearly as possible. "
But it IS meaning that is being conveyed, if only in code. Without code there is no cabal; without code perhaps not even a da Vinci! (Okay, that´s a cheap shot.) The code is the doctrine; the medium the message.
I think that attributing nefarious motives to the art world's use of "Modern" as opposed to "Post Modern" or "Contemporary" is misunderstanding the actual process by which such terms develop.
In music as well, among laymen the term "Classical" represents anything performed in a concert hall or opera house. However, those who study music learn that a style of composition with certain emphasis on form, style of orchestration and melodic/harmonic language emerged toward the end of the era of Bach and Handel, with the music of Haydn, Mozart and early Beethoven best representing what has been termed Classical (pertaining to European music, at least.) As Beethoven and later composers began to push and then exceed the limits of the so-called classical period, emphasis shifted and historians and music critics identified new musical and aesthetic values which they termed "Romantic."
The average person refers to music of Bach, Beethoven, Schubert, Brahms, Wagner, Tchaikovsky and others as Classical, even though to those educated in music there are at least 3 eras of music represented there.
In art, from the Impressionists on, there was such a break with past techniques and goals that the term "Modern" was applied. It covered impressionism, abstract, abstract expressionism, etc. Certainly by the 1960's, new techniques, philosophies and goals in painting, sculpture and other arts began to make clear distinctions in the art that was being made, and the term "Modern," like the musical term "Classical" began to be understood by those trained in art, as a loose body of styles of painting, sculpture and other art media that was qualitatively different from the newer art. "Post Modern" as one descriptor of the differences, was introduced in the art world not as a means of pulling the wool over the public's eyes, but as a means of understanding and describing what had happened in the way many artists now made their work.
You said, "Why not use terminology which is clear so that the rest of the world can understand it?"
In reality, most of the rest of the world is educated in the arts to a degree much higher than what happens in the USA.
Actually, some of the blame for the problem should lie not with the art world for using confusing, or "deceptive" terms, nor with the poorly informed public, but with our attitudes toward education, which has almost totally squeezed the arts out of education, particularly at the elementary school level, but in most educational systems, through high school as well.
I am not trying to "talk down" to anybody here, but the ascription of motives such as deception or worse, I think, are misplaced in reference to the so-called "insider" terminology describing different periods of art.
My firewall is up, so let the flames begin!