Are there continent wide standards for what constitutes a hand free
phone wrt driving?
Short Answer
No.
These rules are established on a state by state basis in the U.S. and otherwise on a country by country or first level of subnational government basis, for the most part.
Long Answer
united-states
Is there some US wide set of rules that if followed is sure to be
count as hands free mobile phone use?
No.
While there are some uniform standards for traffic laws in the U.S., cell phone use is not among them. For example, the law on when minors can use cell phones differs from one U.S. state to another.
In the U.S., the "dormant commerce clause" probably prohibits banning having certain kinds of equipment installed in a car from out of state (or requiring that certain kinds of equipment be installed in a car from out of state) that is merely passing through, although it could have laws against using that equipment in particular ways within that state.
european-union
The European Union didn't, at times when it was relevant, even have a standard regarding which side of the road someone can drive upon. Traffic laws are not within the scope of what the E.U. has fully harmonized between member countries.
The variation in laws isn't maximal
Now, of course, this doesn't mean that there are 53+ actually different substantive rules in North America or several dozen actually different substantive rules in Europe, even though each jurisdiction separately adopted its own rules. There probably aren't even that many reasonable choices of substantive rules on the topic.
Legislators aren't particularly original. Also, there really aren't any deep seated preconceptions regarding phone use in a car that could lead to regional variation, because this is a technology that is quite young. Typically, most jurisdictions will end up following, often intentionally and by design, the laws adopted by the first jurisdictions to pass laws on the topic.
But, as a driver, you can't rely on the law in one jurisdiction on a continent being the same as in another jurisdiction on a continent. There is definitely some variation from one place to another, even within the same continent.