The suggestion was just that: a suggestion. There has never been a definitive statement identifying the woman who washed Jesus’ feet with her tears and Mary of Bethany (the sister of Martha and Lazarus of Bethany) as Mary Magdalene (of Magdala). Some choose to identify them as the same people, others prefer to keep them separate. I believe the Eastern Orthodox distinguish Mary Magdalene from both women, as does the Church (as they have never officially released a dogma stating these women were one and the same), but someone else may know better than I. However, of course, there is certain people who hold the belief they are all the same.
Mary of Clopas (or Cleopas) is the wife of Clopas (or Cleopas), one of the many Marys that are mentioned in the Gospels. In 1982, Stephen Smalley said that it was “very probable” Mary of Clopas was the mother of James son of Alphaeus (James the Less, often confused with James the Great, and may be the same person as James the Just, who was said to the be the ‘brother’ of Jesus), given that Alphaeus/Clopas/Cleopas may be the Greek variation of the Aramaic name ‘Hilfai’. Some people considered her to be Our Lady’s sister, given her name is mentioned after the phrase ‘His mother’s sister’ in The Bible, but this, too, has never been defined, and some consider her to be Our Lady’s cousin (as Hebrew/Aramaic had no word for ‘cousin’ and for the simple question: why would parents name both daughters the same name?) or sister-in-law (being the sister of Joseph).
I hope I helped answer your question; I am sure there are others more knowledgeable than I and may answer this question better.