How to know the difference between two ciphertexts without key stream in stream ciphers
Let's say $C_1 = P_1 \oplus K$ and $C_2 = P_2 \oplus K$ where $P$ is a plaintext, $K$ is the key stream and $C$ is the ciphertext.

Then if you XOR the two ciphertext together you get:

$$C_1 \oplus C_2 =\\
P_1 \oplus K \oplus P2 \oplus K =\\
P_1 \oplus P_2$$

There are all kinds of interesting properties of the XOR of two plaintext together. For instance, one of the most common characters is the space, so you can easily guess many characters by just flipping a bit (space is 0x20 or 0b0010_0000 after all). You can see that a lot of combinations are not possible or unlikely and you can perform frequency analysis.

This becomes even more powerful if you have 3 or more ciphertexts, as you can compare each and every pair, and if there are $n$ ciphertext then there are ${n \cdot (n - 1)} \over 2$ combinations to be made.