Difference between CRC and Hamming Code

I am a bit confused on the difference between Cyclic Redundancy Check and Hamming Code. Both add a check value attached based on the some arithmetic operation of the bits in the message being transmitted. For Hamming, it can be either odd or even parity bits added at the end of a message and for CRC, it's the remainder of a polynomial division of their contents.

However, CRC and Hamming are referred to as fundamentally different ideas. Can someone please elaborate on why this is?

Also why is the CRC compared with the FCS(Frame check sequence) to see if the received message is with or without error? Why not just use the FCS from the beginning? (I might be totally flawed in my understanding by asking this question, please correct me.)

Both CRC and the Hamming code are binary linear codes. One significant difference is that the Hamming code only works on data of some fixed size (depending on the Hamming code used), whereas CRC is a convolutional code which works for data of any size.

So, are CRC and the Hamming code fundamentally different ideas? This is a philosophical rather than a technical question, and so has no definite answer. It could also depend on your point of view. From far away, both are binary linear codes. From up close, there are some crucial differences.

StackExchange Computer Science Q#53719, answer score: 2