To answer this question, we should look at the definitions of each of these words. Using the Merriam-Webster dictionary, we find the following definitions:
redact: (1) to put in writing; (2) to select or to adapt by obscuring or removing information for publication; and (3) to obscure or remove text from a document prior to publication
delete: (1) to remove something from a document, recording or computer files
omit: (1) to leave out, to not include; (2) to fail to do something
Reading these definitions shows us that the words “redact” and “delete” are similar and as such can be used as synonyms in specific situations. To remove something when redacting does contain the further implication that one is doing so in preparation for publication. Thus, a selective author may redact or delete an entire chapter before releasing his book to his publishing house.
That said, someone can delete something without any intention of publication. You may choose to delete half of the five hundred photos stored on your smart phone and it is certain that you are not doing so because you plan to publish the remaining ones.