Headless solutions decouple the interface editing experience (development, web design, architecture...) from content editing.
In the context of a CMS, the aim of headless solutions is (normally) to simplify the content editing process: contributors are concerned only with the content, and have no control over the form. This avoids time-consuming and tedious page-layout work, while guaranteeing graphic unity on your website.
A headless DAM works on the same principle (API call), but meets slightly different objectives. Choosing a headless DAM makes particular sense for companies that want to enable their various teams to mobilize media and other digital assets in their day-to-day tools. For example, a Headless DAM will enable a sales person to access these digital assets in Salesforce, marketing teams to access them in Hubspot, or project managers to mobilize them directly in Monday or Asana.
While there are both Headless CMSs and Headless DAMs, it's also possible to get the best of both worlds by integrating a classic DAM into a Headless CMS.