We say a symmetric key encryption scheme $\Pi_{1} = (\mathrm{Gen}, \mathrm{Enc}, \mathrm{Dec})$ is computational security if for every PPT algorithm $A$ and every $x_{0}, x_{1}$ ($|x_{0}| = |x_{1}|$), $$ \left\vert \Pr\left[\mathrm{Gen}(1^{n})=k; A (\mathrm{Enc}_{k}(x_{0})) = 1\right] - \Pr\left[\mathrm{Gen}(1^{n})=k; A (\mathrm{Enc}_{k}(x_{1})) = 1\right] \right\vert < \varepsilon(n) $$
Is there a definition of computational security of public-key encryption as following?
We say a public-key encryption scheme $\Pi_{2} = (\mathrm{Gen}, \mathrm{Enc}, \mathrm{Dec})$ is computational security if for every PPT algorithm $A$ and every $x_{0}, x_{1}$ ($|x_{0}| = |x_{1}|$), $$ \left\vert \Pr\left[\mathrm{Gen}(1^{n})= (pk, sk); A (pk, \mathrm{Enc}_{pk}(x_{0})) = 1\right] - \\ \Pr\left[\mathrm{Gen}(1^{n})= (pk, sk); A (pk, \mathrm{Enc}_{pk}(x_{1})) = 1\right] \right\vert < \varepsilon(n) $$
Is it equivalence to IND-CPA?