ΔE 20.2, loose: different enough that you should pick on purpose. Old Rose is noticeably darker, more muted, warmer than Hot Pink.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 20). Old Rose is noticeably darker, more muted, warmer than Hot Pink.
The same difference applies the other way round: Hot Pink is noticeably lighter, more saturated, cooler.
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.
See Hot Pink on the colour wheel See Old Rose on the colour wheel
All matches: Hot Pink equivalents · Old Rose equivalents