Purple Rain vs Violet Vamp

How close are they?

ΔE 15.7, loose: different enough that you should pick on purpose. Violet Vamp is noticeably darker, warmer than Purple Rain.

Can I use Violet Vamp instead of Purple Rain?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Violet Vamp is noticeably darker, warmer than Purple Rain.

Can I use Purple Rain instead of Violet Vamp?

The same difference applies the other way round: Purple Rain is noticeably lighter, cooler.

ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.