I'm not sure if I'm calling the thing (key collisions) correctly, and that's probably why I couldn't find any information about it on Google. Still, my question is as follows. Note that I don't work with encryption right now and I'm not going to implement anything based on this knowledge; this is a purely theoretical question which I found very interesting.
Suppose that you have a key
K and a plain text
P. Then you use some symmetric algorithm
A like one of AES variants to obtain a ciphertext
C = A_encrypt(P, K). Is it possible that some key
K* != K exists which can be used to get back the plain text out of the same ciphertext, i.e.
P = A_decrypt(C, K*)? How it depends, if it does, on the type of the cipher (block vs stream), on the exact algorithm and on the size of the key and the size of the plain text? My intuition suggests that impossibility or, at least, improbability of such thing is the reason of existence of symmetric ciphers, but still this is not stated explicitly anywhere I could find.
What surprises me that I couldn't find anything which answers such question directly; moreover, I couldn't find anyone asking such question. All I could find are questions like this which seem to be related but not exactly the same as my question, and questions like "how to generate two keys to decipher the same data" which are somewhat opposite to my question.