Learn English – what is the correct abbreviation for millions, billions and trillions in a financial context

It is highly unlikely that there is a global standard. It differs based on practice and the standards set by the relevant authorities (publishers and the like).

Ex: The Oxford Journal Instructions for Authors suggests (Sec. 2.3):

Abbreviations where the last letter of the singular word is not included take a full stop (vol., vols./ed., eds.). The abbreviation for number is no./nos. Abbreviated unit of measurements do not take a full stop (lb, mm, kg) and do not take a final 's' in the plural.

This is a suggestion from Cambridge Dictionary for use of no. as the abbreviation for number.

The first uses the adjective financial as an adjective (as one would expect, I suppose).

The second uses the noun finance as an adjective.

You're allowed to use nouns in this way, but it is not as commonly done in cases where there is a well-known simple adjective, so we would expect the first to be more common, and it would probably be the better to go for, if you are choosing between using the two.

That said, business-y types seem to have a particular fondness for noun adjuncts. I think they've got the impression that they're more punchy or something. (If so, they are, IMO, wrong, but there's no accounting for taste).