Well one, no, violet is quite a distinct color from magneta (the color you get by mixing blue and red light, i.e., "purple"). They're not hugely far apart, but e.g. on this chromaticity diagram, violet is at the bottom while mixtures of blue and red light form a magenta shade bottom-right of center. Magenta and violet are as different as red and yellow or green and cyan.

But the answer to your question is that you distinguish blues from purples by how different the signals from your M and L cones are. In both colors, the S cones are stimulated. If L > M, you see purples. If L ~ M, you see violet. If M > L, you see blues. At the far violet end of the spectrum, both L and M are near zero. At the far red end of the spectrum, L > M but both are weak, so combining that with blue produces high S, low-but-positive L-M (as opposed to high S, ~zero L-M for violet). The difference L - M is not hugely different between violet and purple, which is why they are similar-ish looking.