Mediumship became quite popular in the 19th-century United States and the United Kingdom after the rise of Spiritualism as a religious movement. Modern Spiritualism is said to date from practices and lectures of the Fox sisters in New York State in 1848. The trance mediums Paschal Beverly Randolph and Emma Hardinge Britten were among the most celebrated lecturers and authors on the subject in the mid-19th century. Allan Kardec coined the term Spiritism around 1860. Kardec claimed that conversations with spirits by selected mediums were the basis of his The Spirits' Book and later, his five-book collection, Spiritist Codification.
In 1880 the American stage mentalist Washington Irving Bishop published a book revealing how mediums would use secret codes as the trick for their clairvoyant readings. The Seybert Commission was a group of faculty at the University of Pennsylvania who in 1884–1887 exposed fraudulent mediums such as Pierre L. O. A. Keeler and Henry Slade. The Fox sisters confessed to fraud in 1888. Margaret Fox revealed that she and her sister had produced the "spirit" rappings by cracking their toe joints.
While I still am unsure why the translucence varies, I believe it’s a mixture of how closely they are still tied to the physical earth (more connected to earth, more ‘earthly’ looking, less connected, more ‘spirity’ looking). I also think it has to do with their skill level at being able to appear and the amount of energy they have to appear - it takes a lot of skill and energy to appear as a human in physical form without an actual physical body to work with!