Hearthborn vs Bright Yellow Ochre

How close are they?

ΔE 16.7, loose: different enough that you should pick on purpose. Bright Yellow Ochre is a little darker, more saturated, cooler than Hearthborn.

Can I use Bright Yellow Ochre instead of Hearthborn?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 17). Bright Yellow Ochre is a little darker, more saturated, cooler than Hearthborn.

Can I use Hearthborn instead of Bright Yellow Ochre?

The same difference applies the other way round: Hearthborn is a little lighter, more muted, warmer.

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.