Left to right: plantains, red bananas, bananitos, Cavendish bananas. - Credit: TimothyPilgrim.
Given that the bananas are green and are boiled before eating, they are probably plantains. Boiled plantain is a staple dish in the Caribbean. Its plain flavour and starchiness mean that it is used in a similar way to the potato in the UK.
As there is no formal botanical distinction between plantains and bananas, the names are used variously in different places (as in the video: what he is cooking is, despite what he says, called a plantain in the UK).
The calabash is a fruit that grows on the calabash tree, native to the West Indies. It has a hard shell that, once the fruit is scooped out, is commonly used as household crockery.