The rules are becoming more and more harmonised.
What is not harmonised is the way that they are enforced in the two jurisdictions.
The USA is a country where aviation has been nurtured from its very beginnings with the Wright Brothers. By and large, the industry is regulated by people who understand aviation and its importance, and operated - with very few exceptions - by people with high standards of honesty and discipline that is bred into them as part of their aviation DNA.
The UK once had that, and in a few secret corners that spirit can still be found. So did some other European countries; France, Italy and Germany both had magnificent pioneers.
But the dead hand of EASA is now laid on the industry in Europe; an organisation as dysfunctional as many of its Member States. Every decision is a political compromise between the divergent aspirations of 27 States; every Member State has to fill a number of posts regardless of ability, and only people with mediocre ability apply anyway. Ever been to Cologne? Enough said.
And in the UK we have the CAA, the last home for the unemployable. Its propensity for shirking any challenge is now well documented. The lack of competence and knowledge among its Inspectors and Surveyors is quite breath-taking; this is partly the foreseeable consequence of its habit of shoeing cronies into these jobs rather than people who earn them by merit.
It is commonly said of these people, quite rightly, that they make up their own rules as they go along to suit their particular - ill-informed - prejudices, and that this stems from ignorance. The result is total inconsistency between their pronouncements; different day, different answer, is the default position. Their stupidity is exacerbated by their arrogance, personal in many cases as well as institutional. The CAA reaches its nadir in the Personnel Licensing Department (Division? Does it matter?) as many will have experienced, where outrageous charges are combined with outrageously bad and slow service.
The CAA is now obsessed with minutiae, while being evidently unaware of the bigger picture of aviation safety. The process is all; the outcome is not their problem, is how they see it, because they are only there to enforce the process. There are things being done every day, now, that are dangerous, by large airlines especially, which the CAA either condones or is unaware of; what they know is that the right boxes have been ticked and their well-padded bottoms are thereby covered.
The CAA's failings extend well beyond Safety Regulation; as an Economic Regulator they are completely ineffectual. You only have to look at the disaster area that is the "London Airport System", and then to consider that if the CAA had been a strong and effective body for the last decade at least things could have been very different.
The CAA used to be openly corrupt; some years ago it was my job in a particular airline, now happily defunct, to give the FOI his new car every year as he ignored the appalling operational practices going on under his nose. Someone else dealt with the maintenance Surveyor. Now, the corruption is more sinister, as its staff cover for each other's incompetence, and "arrange" jobs for their friends. And when did using their victims' fees and charges to fund a private company become part of their mandate?
This rant may or may not be germane to your studies; but I hope it helps to understand the huge differences between the regulatory regimes, while they apply quite similar rules.