A privacy notice is the information you give people about what you do with their personal data. In everyday use it is the same document as a privacy policy, and arguing about the two words wastes time that would be better spent on the distinction that does matter: the difference between a document available somewhere and information given to a person at the moment you collect from them.
Notice, policy, and the useful distinction
Where practitioners separate them, the policy is internal, describing to staff what the organization does, and the notice is external, telling people what is done with their data. Most small companies publish one document and call it either. What is worth keeping from the distinction is the word notice itself: giving notice is an act directed at a person at a moment, not the existence of a page.
What it has to contain
Who you are, what you collect, why, on what basis where a European regime reaches you, who receives it, whether it leaves the country and under what safeguard, how long it is kept, what rights the person has, how to exercise them and how to complain. Under California's consumer privacy statute a business in scope also states the categories sold or shared and the retention period, and carries the routes to opt out and to limit sensitive information.
Where it has to appear, which is the part that fails
At or before the point of collection. A notice at collection sits beside the form, the checkout, the sign-up and the support widget, and links to the full document. The footer link is the permanent address; the contextual link is what discharges the duty. A site with an excellent policy and no notice beside any of its forms has done the writing and skipped the giving.
Other questions people ask
Is a privacy notice the same as a privacy policy?
In ordinary usage, yes. Where the two are distinguished, the policy is the internal statement and the notice is what is given to the person.
Does it have to be long?
No. The requirement is concise, transparent and in clear language. A short notice at collection linking to a fuller document is the shape that meets both the brevity and the completeness expectations.
Can a notice be given verbally?
Where collection happens on a phone call, the information has to reach the person at that point, and pointing them to the published document is the usual way. What matters is that the giving happened, not the medium.