I'd say that the use of the modern English purple has shifted somewhat toward the violet side of the "line of purples" from its Latin origin purpura. This shows how English purple has generalised with the greater range of purple shades physically available. True Tyrian purple, from Bolinus brandaris, is certainly on the red side for my own range of purple, and the more violet shade from Hexaplex trunculus is closer to my ideal.
Note how this differs from the English purpure, which is closer to the Latin in orthography, is only retained in modern English in the field of heraldry, and which William Caxton is 1489 describes as:
Purpre that we calle red representeth the fire the moost noble of all iiii elementes.
Although English violet is used for the spectral colour (thanks to Newton; purpureus was definitely more common in Classical Antiquity and in the Middle Ages), and thus is strictly distinguished in colorimetry, it is not attested in Old English (whereas purple is), and is first attested as the flower in the 14th century, with the colour not long after that.
French prefers the adjective violet, through Latin violaceus, to cover a similar range of colours on the "line of purples". Its noun and adjective pourpre continues to refer to the purple dyes extracted from the murex shellfish, and the historical and liturgical robes of purple, and has extended it in literary use to a dark burgundy-like red. From Leon Dierx, 1867:
La pourpre de la honte au sourire crédule.
Hence the quote from Les mots de couleur : des passages entre langues et cultures that English purple is not the equivalent to French purple:
De même l’anglais purple n’est pas l’équivalent de pourpre
Some of the other Romance languages have words apart from the descendants of Latin viola or violaceus as their most common word for purple: roxo in Portuguese comes from Latin russeus (dark red) but extends across the "line of purples" towards violet, with púrpura staying on the reddish side. Similarly for morado in Castilian Spanish, named for the relatively reddish purple of the mulberry, but also by extension the darker, bluer shade of the blackberry.
As for German, we see that violett (borrowed from French) is the main reference, with lila also being used. Whether they are used interchangeably or not, whether it's a formality or generational difference, or whether it is an actual difference in hue, that seems to be debated. However, it is interesting to see how the German used at the Vienna Natural History Museum describes down the difference in a scientific context.
It is tempting to try to link changes with various historical factors:
- the switch to using cochineal for cardinals' robes in the Roman Catholic Church after the 1453 Fall of Constantinople (and thus the extinction of Tyrian purple in Western Europe)
- the impact of mauveine, originally named aniline purple, discovered/synthesised in London in the 19th century, and sparking a fashion craze as well as the modern chemical industry
- the Munsell color system and modern colorimetry (note how the "line of purples" is Purpurlinie in German and ligne de pourpres in French)
... but I think that the basic preference in the nomenclature in English had been established before these events.
An interesting comparison can be drawn with Chinese 紫色 (zǐsè in Standard Mandarin Pinyin; zi2 sik1 in Cantonese Jyutping; also むらさきいろ murasaki-iro in Japanese), which is derived from the root of the gromwell plant Lithospermum erythrorhizon and has been a basic plant dye from at latest the Spring & Autumn period (its popularity was even a concern for Confucius). The dye can produce very deep purples, close in hue to the purple of mauveine, but it generally tends to lighten and redden over time due to photobleaching. Hence 紫色 even in Modern Chinese can refer to a relatively wide spectrum of hues, and saying 紫蓝色 lit. purple-blue colour or 紫红色 lit. purple-red colour can be fairly common in daily speech.