When I study symmetric encryption, it is quite straightforward to understand the following: in the presence of eavesdropper, simply using a PRG $G(k)$ and XORing multiple messages won't provide indistinguishability in the similar fashion as for a single message.
But what happens for multiple distinct messages? Will a simple PRG $G(k)$ provide indistinguishability?
I know there is discussion on deterministic CPA-secure schemes which could use synthetic IV, etc. But do we really need to go that far?
What is the difference? the distinct messages make the (key, message) pair distinct already? does it depend on how we define indistingushability?