A persistent link is a permanent URL to a specific journal or article within an electronic resource like EBSCOhost, that can be saved and used for future reference. Persistent URLs are designed so that your bookmarks and links don't break when a website gets updated. If you want to bookmark a study page or link to it from your website, you should bookmark/link the persistent URL. In most browsers, you can do this by right-clicking on the link. In the menu that appears, there will be an option to add it to your bookmarks.
DOI stands for Digital Object Identifier (see The DOI System). A DOI is a unique persistent identifier for a published digital object, such as an article or a study. The DOI links you to the article or study. Here is an example of a citation for a study with a DOI:
Deschenes, Elizabeth Piper, Susan Turner, and Joan Petersilia. INTENSIVE COMMUNITY SUPERVISION IN MINNESOTA, 1990-1992: A DUAL EXPERIMENT IN PRISON DIVERSION AND ENHANCED SUPERVISED RELEASE [Computer file]. ICPSR06849-v1. Ann Arbor, MI: Inter-university Consortium for Political and Social Research [distributor], 2000. doi:10.3886/ICPSR06849
The DOI in this example is 10.3886/ICPSR06849 and it links to the URL: https://dx.doi.org/10.3886/ICPSR06849