The relationship is not actually quite the way around you think it is - the naming of senior American Cabinet members actually has a lot in common with both contemporary and modern British naming, and British naming conventions most probably directly inspired American ones.

In the United Kingdom today, all senior Cabinet members - those responsible for heading up a government department - are legally known as Principal Secretaries of State. The minister responsible for foreign affairs and diplomacy is commonly referred to as the 'Foreign Secretary' but his or her full, legal job title is Principal Secretary of State for Foreign and Commonwealth Affairs. Although all of the members of the government tend to be grouped together as 'ministers' in popular culture, in modern Britain this term strictly speaking refers to the more junior political officials who report to a Secretary of State, usually responsible for a very specific area of public policy within a Department's remit. The Secretary of State for Education might for example have a Minister of State for Universities and a Minister of State for Schools reporting to them, with additional Under Secretaries reporting to those Ministers if required.

Although it would sound strange to American ears to hear a member of a President's Cabinet referred to as a Minister today, this was not always necessarily the case. The term 'Minister' had widespread use in the 18th century to describe senior diplomats representing the United States abroad, with the most senior member of a delegation - effectively the equivalent to a modern day official Ambassador - being referred to as a Minister Plenipotentiary. Generally speaking when utilisied by American writers in the 18th century to describe officials the term 'Minister' is used to refer to a diplomat, and this reflects the original meaning of the term in English political history: a position intended to serve and represent the interests of a monarch as an autocratic executive, rather than a semi-autonomous political role. But when Congress was debating what the administration of foreign affairs and public policy might look like, the term 'Minister' was occasionally used where we might now find it unfamiliar. Elias Boudinot addressed the issue of Congress not yet having elected a 'Minister of Foreign Affairs' in a letter written in July 1783, and there are very occasional uses of the term in other ways where 'Secretary' might be used today.

A medievalist could better explain the full history of the use of the term Secretary but suffice to say, by the time Britain's colonies in North America had decided to revolt and begin their own nation-building exercise, the term was one widely used in the political culture and infrastructure of Great Britain. It uses in different forms was still inconsistent in the 18th century and would not be fully, solidly codified until after the Second World War, but the modern political title has its origins in the name given to the role of two advisers and assistants to the English monarch. By the time of the War of Independence there were three Principal Secretaries of State: the Secretary of State for the Northern Department, the Southern Department, and the Colonies. These were roles defined by their geographic authority rather than any particular, singular portfolio of responsibility vis a vis the administration of public affairs. Not long after they gave way to two of the oldest and most important government roles in the Britain: the Secretary of State for the Home Department and the Secretary of State for Foreign Affairs. Some years later a third role was created with responsibility for conflict and colonial affairs, effectively re-establishing the older Secretary of State for the Colonies.

Secretary itself was a perfectly logical title to give senior American officials post-independence then, particularly given the predominantly diplomatic connotations of 'Minister', and there were no senior government posts in Britain at the time where 'Minister' would be the official role title (those not elevated to Secretary of State usually had a very specific job title instead - or sometimes none at all). It essentially recreated institutions and roles familiar already to the populace and to community leaders, rather than trying to construct something completely new and alien, in the same way 'House of Representatives' and 'Senate' both recalled democratic institutions that an educated, voting-eligible member of the new American public would have already been familiar with the intended purpose and value of.

Secretary of State is the job title that causes confusion the most in this context. If Britain had multiple Secretaries of State, how did the US end up with a singular Secretary of State and then a collection of additional Secretaries? The answer, truthfully, is that the Secretary of State title is a bit of a misnomer. The British officials are true Secretaries of State in the sense that their purpose is to act as Secretary, as administrators and monitors of public policy, for areas of State authority. The Secretary of State is perhaps better described in its original formulation as the Secretary for the State - an official who would be responsible, in the words of George Washington trying to persuade Thomas Jefferson to take up the role in 1790, for "the successful Administration of the general Government" beyond the spheres of national defence and financial planning. The role we now think of as Secretary of State began its life very briefly as the the Secretary for the Department of Foreign Affairs, responsible exclusively for American diplomacy, in July 1789. In September of the same year Congress resolved to transform this into the Department of State and afford it all of the general administrative responsibilities lacking a dedicated government department, including the proper recording of both federal and state law for the benefit of all. Some of these domestic obligations - primarily formal ones - still remain with the modern Secretary of State, whilst others have been transferred elsewhere with the growth of the federal government, meaning the title Secretary of State is arguably now a somewhat archaic hangover. For all intents and purposes, the British title Principal Secretary of State and the American title Secretary (when applied to a Cabinet member) are functionally equivalent to one another with only a handful of exceptions. Today this is one of the few exceptions to the aforementioned rule of equivalence: the British counter-part to the Treasury Secretary is now the Chancellor of the Exchequer, with the Chief Secretary to the Treasury acting more as a Deputy Finance Minister in the UK.

Other roles and titles were likely borrowed directly from their British counter-parts. The Secretary for the Treasury, for example, is a clear copy-and-paste job from the equivalent and contemporary British title of Secretary to the Treasury. Britain at the time did not have a fixed finance minister - indeed, the job we now call Prime Minister was once First Lord of the Treasury (a job the PM still officially holds today), and the very distinct role of Chancellor of the Exchequer (today Britain's Finance Minister) did not really exist as we understand it today - but did have at least two Secretaries responsible for assisting in the financial affairs of government. Benjamin Franklin was a friend of a politician by the name of Grey Cooper who was a prominent Secretary to the Treasury for many years; that relationship may have particularly influenced the naming of the Treasury Secretary's role but in any event, there was an obvious counterpoint in British political culture for naming the official responsible for the financial affairs of the government.

There is probably more to say here about what influence the French convention of using titles like Minister of State may have played in shaping the naming conventions of American politics but that would be outside my wheelhouse and fundamentally, the use of the term Secretary represents a duplication and reproduction - rather than a refutation - of naming conventions in Britain. 'Secretary' was most likely simply a convenient familiar title that would be quickly and easily recognised in its purpose. It's worth pointing out that similar roles existed in the very early American Republican for the legislative branch. The Secretary of the Senate predates the Secretary of State as a role and still exists today, with responsibility for ensuring the smooth administration and day-to-day running of the Senate as an institution, whilst the equivalent Clerk of the House of Representatives is essentially a recreation of the earlier role of Secretary to the Continental Congress. Although now a ceremonial process, both roles are formally elected and both roles have extremely significant responsibilities to ensure the proper functioning of the legislative branch of government. Though their ability to make any kind of autonomous decision is limited compared to those heading up a government department in the executive branch, they are essential to the day-to-day functioning of American democracy, and share an essence of character with their executive counterparts in the sense of being responsible for making sure entire divisions of public administration can function properly.