"Explicit", "classified", "graphic" - did these words originate as abbreviations of longer phrases?

The way these meanings got attached to the words is speakers using shorthand and listeners making assumptions based on past experience.

So people said “[sexually] explicit” enough times that the word explicit gained the additional meaning “[sexually] explicit.” Same with your other examples.

However, keep in mind that when you say “graphic [violence]” I hear “graphic” because I sometimes work as a graphic artist. Context matters.