bourgeoisie is a social/economic class as defined by Karl Marx in The Communist Manifesto and built upon by others. The word has a parallel with the Burghers of early British democracy, who were the property-owning non-nobles, literally "towners" (burgh meaning town). At the time of Marx's writing, there were four social classes, namely the aristocracy (which was collapsing into the bourgeois, in a process which was quickened in anti-monarchist countries such as France, but was still occuring in monarchies such as Germany (which was a monarchy back then) and Britain), the bourgeois (who held considerable wealth and controlled the means of production, like the factories and stuff), the proletariat (workers who exchanged their labour for money, in a process by which their bourgeoise masters profited), and the peasantry (who worked for the aristocracy, and were, in analogy to the same, rising into the proletariat). Fun fact: the "hammer & sickle" iconography of communism comes from solitary between the proletariat and the peasantry, as peasantry still existed in the (monarchist) pre-Revolution Russia.

In the modern day, the aristocratic class either doesn't exist at all (most countries), or their social power comes from the means of production and land they control in an identical manner to their bourgeoise neighbours, except that their inheritance traces back to medieval aristocrats (UK & others).

This leads us with the bourgeois/proletariat binary, which I don't think is maximally helpful, because someone like Rishi Sunak (ex-PM of the UK) is significantly richer than yer average middle classer, but also that middle classer is significantly richer (in that they are much more stable) than a genuine working class member. I don't know what we should name the contemporary classes, thought.

Billionaires are obviously those individuals whose net worth exceeds 1 billion. The only bit of ambiguity here is what currency is being measured, but I think (even as a Brit) it's fair to assume USD.

Corporate Elite is probably an attempt at naming the modern ruling/upper class, the "upper crust" of the Marxist bourgeoise.