Practically speaking, public access (i.e., free online access to research, for everyone) includes researcher access (free online access to research for researchers).
Moreover, free online access to research, for everyone, includes both public access and researcher access.
So what difference does it make what you call it?
The answer is subtle, but important:
The goal of providing “public access to publicly funded research” has a great deal of appeal (rightly) to both tax-paying voters and to politicians.
So promoting open access as “public access” is a very powerful and effective way to motivate and promote the adoption of open access self-archiving mandates by public research funders such as NIH and the many other federal funders in the US that would be covered by the Federal Research Public Access Act (FRPAA).
That’s fine for publicly funded research.
But not all research — nor even most research — is publicly funded.
All research worldwide, however, whether funded or unfunded, originates from institutions: The universal providers of research are the world’s universities and research institutes.
To motivate institutions to adopt open access self-archiving mandates for all of their research output requires giving them and their researchers a credible, valid reason for doing so.
And for institutions and their researchers, “public access to publicly funded research” is not a credible, valid reason for providing open access to their research output:
Institutions and their researchers know full well that apart from a few scientific and scholarly research areas (notably, health-related research), most of their research output is of no interest to the public (and often inaccessible technically, even if accessible electronically).
Institutions and their researchers need a credible and valid reason for providing open access to their research output.
And that credible and valid reason is so as to provided access for all of the intended users of their research — researchers themselves — rather than just those who are at an institution that can afford to subscribe to the journal in which it was published.
Subtle, but important.
It has become obvious that the >75% of researchers who have not been providing open access to their research for over two decades now — despite the fact that the Web has made it both possible and easy for them to do so — will not do so until and unless it is mandated. That’s why mandates matter.
The rationale for the mandate, however, has to be credible and valid for all research and all researchers. “Public access to publicly funded research” is not.
But “maximize researcher access to maximize research uptake and impact” is.
And it has the added virtue of not only maximizing research usage, applications and progress — to the benefit of the public — but public access to publicly funded research also comes with the territory, as an added benefit.
So Mike Rossner (interviewed by Richard Poynder) is quite right that the two are functionally equivalent.
It is just that they are not strategically equivalent — if the objective is to convince institutions and their researchers that it is in their interest to mandate and provide open access.