To answer the question in this post "What is the historical reason why there is this transatlantic difference?":
Zucchini - Italian word used in USA
As a result of the large wave of Italian immigration to the United
States in the late 19th and early 20th centuries, Italian and Sicilian
were once widely spoken in much of the U.S.
Courgette - French word used in UK
During the Norman occupation (1066), about 10,000 French words were
adopted into English, some three-quarters of which are still in use
today. This French vocabulary is found in every domain, from
government and law to art and literature.
American Italian Language
French Influence On English