You have it backwards. Purple is a fancy synonym for dark magenta.

Purple is attested as a color name in English for about 600 years.

Before that, it has been used as a color name in various languages that have borrowed it from Latin or directly from Greek, where it had been used for about 3000 years or more.

Magenta has been used as a color name in English since 1860, "named in honor of the Battle of Magenta in Italy, where the French and Sardinians defeated the Austrians in 1859".

Initially, magenta was not a generic color name, like today, but it designated a certain cheap aniline dye, of purple color.

So purple cannot be considered a synonym for the neologism "magenta". Magenta could be considered as a certain specific shade of purple, except that during the time it has been applied to different dyes, depending on the evolution of dye technology, so the word "magenta" has not meant always the same color, but at most a range of purple colors that was never defined precisely.