Barren Yellow vs Yellow Ochre

How close are they?

ΔE 20.0, loose: different enough that you should pick on purpose. Yellow Ochre is noticeably lighter, more saturated than Barren Yellow.

Can I use Yellow Ochre instead of Barren Yellow?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 20). Yellow Ochre is noticeably lighter, more saturated than Barren Yellow.

Can I use Barren Yellow instead of Yellow Ochre?

The same difference applies the other way round: Barren Yellow is noticeably darker, 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.