Is a privacy policy the same as a privacy notice?

In most cases yes, but not always. A privacy policy on a website is often referred to as a 'privacy notice' and they are the same thing, such terms being used interchangeably.

However, it is possibly for an organisation to have an internal privacy policy that is not posted on a website. In that case, it would be known only as a privacy policy and not a privacy notice.

Source: GDPR Privacy Policy, the leading provider of GDPR-compliant website documentation - gdprprivacypolicy.org