Apothecary White vs Dark Turquoise

How close are they?

ΔE 50.9, loose: different enough that you should pick on purpose. Dark Turquoise is noticeably darker, much more saturated than Apothecary White.

Can I use Dark Turquoise instead of Apothecary White?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 51). Dark Turquoise is noticeably darker, much more saturated than Apothecary White.

Can I use Apothecary White instead of Dark Turquoise?

The same difference applies the other way round: Apothecary White is noticeably lighter, much more muted.

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.