At a high level NDAs basically say "do not disclose confidential information to the public". At a high level Non-disparagement agreements basically say "do not disclose information to the public that could harm us". Both are trying to protect the company from damage caused by information getting into the wrong hands. For example if a bank was hacked into and lost a bunch of money, wouldn't both NDA's and non-disparagement agreements prevent employees from telling the public about it? I guess NDAs are more about facts where as Non-disparagement include negative opinions.In a sense are all non-disparagement a type of NDA because they are prohibiting what could be said?
Not all disclosures are disparagements, an NDA will typically cover the release of any private information, whether positive or negative. Publishing the company's future product plans might violate an NDA but would not be disparagement.
Not all disparagements are disclosures, a negative opinion does not require the release of any private information. Making a blog post stating your opinion that the company's CEO is incompetent or that their products are overpriced is likely not disclosing any private information that would be covered by an NDA, but is disparagement.
In the employment context:
A non-disparagement agreement: the signatory agrees not to say anything negative about the employer or its staff, goods or services.
A non-disclosure agreement: the signatory agrees to not reveal to anyone information the employer wants to keep secret. For example, financial information, customer data, trade secrets, marketing and pricing strategies, techniques and costs, operating information and costs like payroll, suppliers etc.
Things a company might prefer to be secret are not necessarily negative about the company. They could be neutral. They could be positive - for example, the progress of a cure for some cancers.
Both positive and negative information about a company might hurt them if it becomes public and is therefore meant to be covered by an NDA. But damage isn’t needed. If I say something that nobody cares about, or that actually helps the company, that would still be covered by sn NDA except I wouldn’t be likely to be sued.
Positive information will often not be disparaging and will not be covered by a non-disparagement agreement. (But making lots of money by legally exploiting a customers naivety might be positive and disparaging at the same time). Negative information may be already known to the public but repeating it would still be disparaging.
And I should really ask a question whether false statements are covered by an NDA. I’m sure negative statements could be disparaging whether true and false and covered either way.