"Financier" in British and American English

I am teaching English to a group of university students whose major is Finance, and whose native language is not English. I have no background in economics in general or finance in particular. I am from Britain.

My students often refer to their future career as 'financiers'. This didn't seem right to me, as I has always understood financiers to be people who provide finance (ie capital) from their own resources.

The Oxford Advanced Learner's Dictionary confirms my feeling, as it talks about "providing" money, though not explicitly from one's own resources:

financier (...) a person who provides money for businesses etc. on a large scale.

However, a trip to the Wikipedia article on financier made me wonder if there is a broader definition of 'financier' to include people who make a living out of finance, whether or not they are dealing with their own or others' money. I also wondered if the confusion might be because there is a difference in British and American usage.

Merriam-Webster is my usual go-to for American usage. Here I found:

1 one who specializes in raising and expending public moneys

2 one who deals with finance and investment on a large scale

The definitions here seem to be broader than that of the Oxford Learner's Dictionary, though the categories of 'public moneys' and 'large scale' seem to provide some limitation which might not cover all professional applications of a degree in Finance.

The link from that site to the Merriam-Webster learner's dictionary gave:

a person who controls the use and lending of large amounts of money

Again, quite broad, but again the limitation of "large amounts of money".

My question: Are my students right to refer to their future career as 'financiers' even if they are not planning to finance things from their own resources? Is there a difference in American and British usage here?

In addition to the dictionary entries cited in the question here is an article from a well-known financial magazine that implies that it doesn't have to be their own money. It also uses the term financial professional which might be more general than financier for Finance majors.

From Forbes magazine:

In return for a fee the financier plays the role of pooling the money from those who have it¹ and distributing it to those who need it. Since they are at the center of the flow of money to consumers, governments and businesses, financiers control the lifeblood of the economy.

¹emphasis mine