Bright Slate Grey vs Templar White

How close are they?

ΔE 18.2, loose: different enough that you should pick on purpose. Templar White is noticeably lighter, more muted than Bright Slate Grey.

Can I use Templar White instead of Bright Slate Grey?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 18). Templar White is noticeably lighter, more muted than Bright Slate Grey.

Can I use Bright Slate Grey instead of Templar White?

The same difference applies the other way round: Bright Slate Grey 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.