Difference between CRC and Hamming Code
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.