Indigo color is created by mixing more parts of Blue than Red.
Violet color is created by mixing more parts of Red than Blue.
Purple is created when two wavelengths are visible at the same time, between Red and Blue. At the same time, Violet colors border on Red, and Indigo colors border on blue.
Therefore, Purple is a color inbetween Violet and Indigo.
All of what you have said is incorrect. I can't fault you for forming a hypothesis on this though, colors are weird and can be difficult to understand, with the spectrum as one way to define, then RGB/CMYK being the way colors are calculated for screen/print, it can be confusing. When talking about a rainbow we are talking about the visible light spectrum.
Indigo is a shade in between blue and violet. There is no red in indigo, just as there is no red in green. There is also no red in violet.
"Purple" is just magenta; it is a mix of red and blue, it is not on the spectrum at all and is actually your eyes/visual cortex seeing both colors at the same time overlapping.