A hash is a small, lossy representation of a data point. Typically hashes are fixed-sized representations of variable-sized data.
Cryptographic hash functions take and data and return fixed-size representations. These typically have the property that the hash value (ideally) reveals no information about the original piece of data.
The MD5 hash for the string
5d41402abc4b2a76b9719d911017c592, but the hash for
8b1a9953c4611296a827abf8c47804d7. It is typically not trivial to infer that these two distinct-looking hashes have similar inputs.
Semantic hashes are the opposite – they are fixed-length representations where similar pieces of input data should have similar hashes. Word embeddings are a type of semantic hash for words. Words that occur in contexts end up with similar embeddings.
Semantic hashes are useful for document search, information retrieval, or other problems where one needs to find similar pieces of data.