Here are the Wikipedia articles on purple, scarlet, and crimson. Crimson is bluer than scarlet. Purple is bluer still, according to these articles. All three of these, unlike brown, are colors of the rainbow. There are, I'm sure, differences of opinion as to what is purple, what blue, what red, what scarlet, and what crimson.
Easton's Bible Dictionary has an interesting article on colors in the Bible. It says that both purple and scarlet were worn by the wealthy and important. Purple was worn by kings.
Purple occurs 48 times in the Bible. 26 of these are in combination with blue and scarlet, in various fabrics associated with temple worship. Most of the other references have to do with clothing worn by royalty, including Jesus, who was mockingly given a purple robe to wear (John 19:2, 5). Lydia, perhaps the first convert to Christianity in Europe, was a merchant of purple cloth (Acts 16:14).
Scarlet occurs 52 times in the Bible. Half of them are in the combination of blue, purple and scarlet, as above. Scarlet is used to describe our sins in Isaiah 1:18. Scarlet thread is used in rituals for cleansing, especially in Lev 14:4-52. Rahab hung scarlet thread in her window, so that her family would be spared when Jericho was taken. (Joshua 2:18, 21) Scarlet thread was used to identify the first-born twin when Tamar had Judah's sons. (Genesis 38) There is a woman in Revelation, who sits on a scarlet beast, and wears scarlet. (Chapter 17)
Crimson occurs five times in the Bible. Three of them are in II Chronicles 2:7 through 3:14, referring to temple furnishings. One is in Isaiah 1:18, where our sins are compared to both scarlet and crimson, probably for emphasis, but where they will be made white. (There are several songs that speak of the transition from crimson, or scarlet, to white.) The fifth is in Jeremiah 4:30, where it says that even though Israel clothes herself in crimson, she will be punished.
Vine's Expository Dictionary of New Testament Words (accessed through the Blue Letter Bible) says that the word for crimson is derived from an Arabic name for an insect which was the source of scarlet dye. Easton's Bible Dictionary (also accessed through the Blue Letter Bible) says that scarlet and crimson "were the firmest of dyes, and thus not easily washed out."
Roman Catholics have used purple to indicate penance. As I write, there are many churches that have placed a purple cloth draped over a cross on their lawns, to commemorate Christ's suffering.
Here's an example of blood being scarlet, or at least redder than red:
"Son of Adam," said Aslan, "go into that thicket and pluck the thorn that you will find there, and bring it to me."
Eustace obeyed. The thorn was a foot long and sharp as a rapier.
"Drive it into my paw, son of Adam," said Aslan. . . .
"Must I?" said Eustace.
"Yes," said Aslan.
Then Eustace set his teeth and drove the the thorn into the Lion's paw. And there came out a great drop of blood, redder than all the redness that you have ever seen or imagined. And it splashed into the stream over the dead body of the King. . . . And the dead King began to be changed. His white beard turned to grey, and from grey to yellow, and got shorter and vanished altogether; and his sunken cheeks grew round and fresh, and the wrinkles were smoothed, and his eyes opened, and his eyes and lips both laughed, and suddenly he leaped up and stood before them--a very young man, or a boy. . . . And he rushed to Aslan and flung his arms as far as they would go round the huge neck; and he gave Aslan the strong kisses of a King, and Aslan gave him the wild kisses of a Lion. C. S. Lewis, The Silver Chair, New York: Macmillan, 1953, pp. 203-4.
U. S. military personnel wounded in combat may be given a purple heart. There is a bird named the purple
Nathaniel Hawthorne wrote The Scarlet Letter, wherein Hester was forced to advertise her adultery by wearing a scarlet A, and Sir Arthur Conan Doyle wrote A Study in Scarlet. Scarlet fever is an infectious disease. There is a bird named the scarlet tanager.
Alabama sports teams are known as the Crimson Tide. Harvard publishes a newspaper called the Harvard Crimson.
Scarlet, crimson and purple have a lot of significance. They signify the cleansing blood of Christ, royalty, and being specially marked.
Thanks for reading!