X and Y are metal nitrates. X on heating liberates O₂ only but Y on heating liberates NO₂ and O₂. X and Y are respectively

For nitrate of sodium metal:

$2{\mathrm{NaNO}}_3\to 2{\mathrm{NaNO}}_2+{\mathrm{O}}_2$

For nitrates of alkaline earth metals:

$$\begin{gathered} 2\mathrm{M}{\left({\mathrm{NO}}_3\right)}_2\to 2\mathrm{MO}+4{\mathrm{NO}}_2+{\mathrm{O}}_2 \\ (\mathrm{M}=\mathrm{Be}, \mathrm{Mg}, \mathrm{Ca}, \mathrm{Sr}, \mathrm{Ba}) \end{gathered}$$

Therefore, X is NaNO₃ and Y is Mg(NO₃)₂.