Triumphant Navy vs Asheth Grey

How close are they?

ΔE 26.6, loose: different enough that you should pick on purpose. Asheth Grey is a little darker, much more muted than Triumphant Navy.

Can I use Asheth Grey instead of Triumphant Navy?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 27). Asheth Grey is a little darker, much more muted than Triumphant Navy.

Can I use Triumphant Navy instead of Asheth Grey?

The same difference applies the other way round: Triumphant Navy is a little lighter, much 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.