The difference between lobbying and advocacy is that “lobbying” is a type of advocacy specific to influencing a legislator. “Advocacy” is a more general term related to activism on behalf of an issue.
Non-profit organizations are not allowed to lobby; however, any private citizen may write a letter to a legislator with her/his own letterhead. So one must be careful on the letterhead you are using to write your letter and whether you are on company time!
"Lobbying" has a strict legal and IRS definition for nonprofits, which generally only includes activities that ask policymakers to take a specific position on a specific piece of legislation, or that ask others to ask the same. In contrast, the common language definition of lobbying usually includes any discussion of issues with policymakers.
"Advocacy" encompasses any activity that a person or organization undertakes to influence policies. There is great latitude in this definition, and some people consider advocacy to be all activities that are not specifically lobbying, such as public demonstrations, or the filing of friend of the court briefs.
Citizens can both lobby and practice advocacy. It is a good idea to become familiar with the legislative system, especially in public health. There are a number of good resources to help you influence a politician or an issue. In addition, you can advocate for issues that concern you through associations and organizations.
A number of organizations have tips on writing letters to legislators and how to arrange for visits, etc. I am not advocating any of these organizations, but some of these websites have good tips on writing legislators, including sample letters, etc.
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