The first kind of Open Access (OA) button is the “request eprint” button, built into EPrints institutional repository software (or, the request copy button in DSpace software). This button has also been referred to as the Fair Dealing Button, or the Fair Use Button.
Stevan Harnad has, especially since 1994, been a passionate advocate for OA. He has also repeatedly pointed out the virtues of Green OA, preferably via an Immediate-Deposit/Optional-Access mandate (ID/OA). This mandate is based on the deposition of articles into freely-accessible institutional repositories.
The second kind of button is the recently-launched (November 18, 2013) Open Access Button. It was created by two undergraduates from the U.K. (See: Students Launch “Button” to Put Denied Access to Research on the Map).
This second button should not be confused with the first. The latter button is a browser-based tool that can map who is denied access to a research article. (See: Tracking and mapping the impact of paywalls one click at a time).
The two students are David Carroll and Joseph McArthur. They co-authored an article in which they described their reasons for undertaking this project. The article is: The Open Access Button: It’s time we capture individual moments of paywall injustice and turn them into positive change (published on September 2, 2013).
Does it matter that there’s some ambiguity about the term “OA button”? Probably not. There’s already much confusion about OA, confessed by supporters of OA as well as by non-supporters. See, for example, Open Access Headaches by Stephen Curry (November 3, 2013) and Open Access on the Sea of Confusion by David Wojick (November 11, 2013).
It’s the major policy issues about OA that matter the most. A few more drops of ambiguity in a reservoir of uncertainty seems unlikely to make much difference. The OA policy situation here in Canada is illustrated by: NSERC, SSHRC want feedback on open access. Excerpts: “The major research funding agencies in Canada are looking for feedback on a policy that will require federally-funded research in peer-reviewed journals to be freely available to the public within one year of publication” and “The Tri-agency Open Access Policy is modelled after the open access policy at the Canadian Institutes of Health Research, which went into effect in 2008“.
Disclosure: During 2006-2007, I chaired the Advisory Committee on Access to Research Outputs of the Canadian Institutes of Health Research (CIHR). Amendments were made, effective January 1, 2013, to the CIHR Open Access Policy, formerly known as the Policy on Access to Research Outputs. (It’s the Governing Council of the CIHR that decides policy, not an advisory committee).
Be openly accessible or be obscure 
Two Different Kinds of Open Access Buttons | Op... said
[…] The first kind of Open Access (OA) button is the "request eprint" button, built into EPrints institutional repository software (or, the request copy button in DSpace software). This button has also… […]