Nope. All your units are old English units.
As mentioned above, the US system was based on the earlier English unit system, that predated the Imperial system (the Imperial system didn't come into being till well after US independence).
So both systems have a common ancestor, the old English units, why else do you think they use the same names?
The gallon originally (predating the USA), came in several sizes, depending on what you were measuring, there was a wine gallon, an ale gallon, a corn gallon etc etc. (The gallon was used for liquids and dry items).
The US, who was using the English units initially (after all they were an English colony), after independence and wanting to standardise measurements, decided having multiple gallons was a bit silly (quite rightly), so decided to standardise on a single main gallon size, and chose the wine gallon, dropping all the others.
Later on in Briton, when the Imperial units were standardised, they did the same, but based it on the ale gallon instead, dropping all the other gallons.
That's why the US and UK now have different sizes of gallon. They were both derived from old English units, we just picked different ones to use as the standardised gallon.
This is also why other measurements such as quarts and pints are different, as those are divisions of the gallon. A quart being a single quarter of a gallon, and a pint being one half of a quart.
So for example US and UK both have 8 pints in a gallon, just the UK pints are bigger, because the UK gallon is bigger, which sometimes catches out the tourists, if they hadn't noticed before a night out :-)