When all three wear the cassock, things can get confusing.
Outside of the liturgy, clergy members have various options of clothes to wear. For casual occasions most wear the simple black shirt with a white roman collar.
When attending more formal events, or when walking through St. Peter’s Square in Rome, bishops, cardinals and monsignors can wear a cassock that is indicative of their office. Their cassocks each have distinctive colors, but from afar are not easily distinguishable. It is even more difficult when these officials wear a black cassock with only the piping and sash being a different color.
Here is a quick guide to help identify each color and its symbolism.
For many centuries the pope was accustomed to grant honorary titles to priests within his Papal Court. There were numerous degrees of honors, typically only given to priests who worked closely with the Holy Father in Rome. This title was expanded over time and given to priests outside of Rome through the recommendation of a bishop, but was recently limited again by Pope Francis, returning to the older practice.
Being members of the Papal Court, monsignors wear the color purple. Typically monsignors do not have a zucchetto (the skull cap) or a pectoral cross, which distinguishes them from bishops and cardinals.
This color purple (which is closer to magenta) was connected to the tradition in the Roman empire to vest new dignitaries with a purple toga. In medieval heraldry the color symbolized justice, regal majesty and sovereignty.