Tyrian Navy vs Black

How close are they?

ΔE 22.0, loose: different enough that you should pick on purpose. Black is noticeably darker, more muted than Tyrian Navy.

Can I use Black instead of Tyrian Navy?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 22). Black is noticeably darker, more muted than Tyrian Navy.

Can I use Tyrian Navy instead of Black?

The same difference applies the other way round: Tyrian Navy is noticeably lighter, 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.