So, can you tell me the difference between an uncompressed and a compressed address ? I don't even know if I am asking the question properly
We say compressed/uncompressed address to say if address was generated from compressed or uncompressed form of public key.
The address is generated exactly the same way - some input is hashed sha256, encoded with base58 etc.
The difference is what the input is. Public key is in fact a point in 2 dimensions, so you may think it is like (x, y). But, all the points are on the given curve, which is symmetrical, we may say if we have point (x, +y), we may also have point (x, -y) [they are not exactly +-, as symmetry is not on '0 level', but you feel the difference I hope].
So, in the far far past, what was used was point uncompressed, where you hashed XY, and there was prefix 0x04, so content for hash was 04XY. Then, for simplicity, compressed addresses became more popular and now they are almost mandatory (you cannot generate (native)Segwit address from uncompressed public key).
Compressed public key looks like 02X or 03X, where 02 and 03 are 'markers' if you have public key which could be 'extended' to (X, +Y) or (X, -Y).
As for given X it is obvious what Y is, the only question is if it is + or -.
