Before the flower "pink" came to be used to describe colours, pink things were probably called red, in fact. Languages vary in how many basic colour terms they have, and English is exceptional in having (about) eleven. Most have less.

The smallest number of basic colour terms is two (warm/dark vs cool/light). Some languages have three, with red as the third term. Then blue/green is the fourth. A language that has six colour terms almost certainly has black, white, red, yellow, green, and blue.

Beyond that, it varies. We have grey, brown, purple, pink, and orange, for a total of eleven. At least, Roget's use those eleven. Many English-speakers would agree they have those eleven. But it does vary a bit from person to person. Some would say purple was a kind of blue, orange was a kind of yellow or red.

By "basic" I mean a set of shades. If you own a scarlet car, you own a red car. If you own an ultramarine or cerulean pencil, you own a blue one. (Here's the answer to another post here: purple is the generic term covering mauve, lavender, and violet, as well as being a specific shade in contrast to violet or mauve.)

Historically you can see the expansion of the English colour system. In Old English there were the six most fundamental colour terms, plus grey and brown. Then came purple (originally = crimson, the dye from the porphyry or murex), and pink from the flower, and orange from the fruit. These have became basic terms in modern English, so for most people, if something is pink, it isn't red. (Ignore borderline cases: think of the pinkest pink and the reddest red. It's been demonstrated across languages that's its focal shades, not borders, that are important for colour naming.)

This usage is influencing other languages. The European equivalents rose, orange etc are increasingly used as distinct colour names rather than shade names.