Nope. Purple is a wavelength that partially triggers both the red and blue cones.
The visual spectrum is continuous, not just three wavelengths corresponding to the three cones.
The blue cones and the red cones are stimulated by purple light. It’s a mix of blue and red signals from the retina, but the light is a single wavelength that is actually purple.
No, purple is a non spectral colour meaning it is incorrect to call it "a wavelength" but rather you say it is a perception of multiple wavelengths. Not that this is special, pretty much everything you see is a non-spectral colour.
Purple is what you get when you force the visible light spectrum into a wheel, so there'll be something that "connects" blue with red?
If so, is the reason we perceive green as a different color than purple is because we have receptors for that specific wavelength, otherwise both colors would affect our red and blue color receptors similarly?
Essentially, yes. Although violet is a colour, and that does correspond to a wavelength of light. I'm not really sure where violet ends and purple begins.
Looks like this guy has had a crack at explaining the difference, though.