Hate and hatred are synonyms but are used in different ways. Hate and hatred have similarities and differences.
Hate is most common in fiction corpus. Most common collocates of hate are mail, crimes, and admit. The most common phrase for hate is “hate to~”.
Hatred is most common in fiction corpus. Most common collocates of hatred are visceral, mistrust, and sow. The most common phrases of hatred is “hatred for~” and “hatred of~”.
The two are similar in ways that they are most common in fiction corpus. Also, the word that follows each word commonly is a preposition for both. However, looking at the collocates of each word, it is clear that hatred is used with more advanced words than hate. The numbers of frequency also shows that hate is more commonly used than the word, hatred.
Reference:
Davies, Mark. (2008-) The Corpus of Contemporary American English: 450 million words, 1990-present. Available online at http://corpus.byu.edu/coca/.
