question on encryption of multiple distinct messages 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?

Thanks!
It does not work either. There are a few counter examples:

Let $x=G(k)$ be the key stream, which I understand you want to use to encrypt multiple messages

1 $m_1=0^l$ and $m_2=r \in\{0,1\}^l$, once you encrypt $m_1$, the ciphertext $m_1\oplus x = x$ is exactly the key stream, that can be used to decrypt the ciphertext of $m_2\oplus x\oplus x=m_2$. Note $m_1$ and $m_2$ are distinct.

2 Let $m \in \{0,1\}^{l-1}$, $m_1=m||0$, $m_2=m||1$, $m_3 =r \in\{0,1\}^l$, then given the ciphertext of $m_1$, in a CPA game, the adversary can easily distinguish $m_2$ and $m_3$. All 3 messages are distinct.

The main problem is that distinct means the messages are not equal, but nothing more on their distributions. Therefore, it is insufficient to ensure the indistinguishability of ciphertexts.

When you use an iv, which is a long enough random string, the iv is used as input to $G$ (well I am abusing the syntax a little bit), so you have $G(k,iv)$ which produces a different and independent key stream per iv.