Thunder Storm vs Purple Black

How close are they?

ΔE 22.4, loose: different enough that you should pick on purpose. Purple Black is noticeably lighter, more muted than Thunder Storm.

Can I use Purple Black instead of Thunder Storm?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 22). Purple Black is noticeably lighter, more muted than Thunder Storm.

Can I use Thunder Storm instead of Purple Black?

The same difference applies the other way round: Thunder Storm is noticeably darker, more saturated.

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.