APA, MLA, and Chicago formats require "http://doi.org/" or "https://doi.org/" before the DOI number/letter string.
AMA does not require "https://". Instead, you must put "doi: " before the number/letter string. Be sure to include a space between "doi:" and the string.
DOI stands for "digital object identifier"; URL stands for "uniform resource locator." Both are hyperlinks, but DOIs are more authoritative. URLs can change overtime, while DOIs are permanent. Always use a DOI over a URL.
Not every source will have a DOI; if you cannot find a DOI, you can use the URL.
DOIs are not related to the peer-review status of an article. A peer-reviewed article and a non-peer-reviewed article can both have DOIs.