Tyrian Navy vs Dark Blue Black

How close are they?

ΔE 15.7, loose: different enough that you should pick on purpose. Dark Blue Black is noticeably darker, more saturated, warmer than Tyrian Navy.

Can I use Dark Blue Black instead of Tyrian Navy?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Dark Blue Black is noticeably darker, more saturated, warmer than Tyrian Navy.

Can I use Tyrian Navy instead of Dark Blue Black?

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