The main definition of computational indistinguishability is that, for any ppt $A$, and distribution ensembles $\{C_n\}, \{D_n\}$, $$\bigg| \Pr_{x\sim C_n}[A(x) = 1] - \Pr_{x\sim D_n}[A(x) = 1] \bigg| \le negl(n)$$
Sometimes, one sees the following def. A gets a random "challenge" $x$ from $C_n$ w.p. 1/2 or $D_n$ w.p. 1/2. If no $A$ can output 1 with probability greater than $1/2+negl(n)$ when the challenge is from $C_n$ (and 0 otherwise), then $C_n, D_n$ are comp. indist.
Are they equivalent? What is the difference? What is the reduction between them?
