A duchy is the jurisdiction of a Duke. You'd have to check out the specific duchy for more detailed information. A good place to start is the British Royalty website.
Duchy of Savoy ended in 1713.
United Baltic Duchy ended in 1918.
Since the first duke of England was the Duke of Cornwall, the son of Edward III, 1337, I'm going to assume that the first Duchy would be the same, Duchy of Cornwall. The Duchy of Lancaster is held by the Soverign. in Lancaster the toast, "To the Queen, Duke of Lancaster" that's "Duke" not Duchess.
A barony is within a county or duchy. I suppose it would be possible for a barony not to be so, but I have never heard of it.
duchy
A duchy
Duchy of Racibórz was created in 1172.
Duchy of Silesia ended in 1918.
Duchy of Silesia was created in 1163.
Duchy of Westphalia was created in 1180.
Duchy of Bielsko was created in 1572.
Duchy of Głubczyce was created in 1172.
Duchy of Zator was created in 1454.
Duchy of Zator ended in 1919.
Duchy of Limburg was created in 1065.
Duchy of Limburg ended in 1794.
Duchy of Friuli ended in 828.