These are known as the short scale and long scale systems respectively. Though the United States was indeed the first English-speaking country to switch to short scale, pretty much all English-speaking countries have used short scale almost exclusively for a long time, including the United Kingdom. Saying that it's simply being influenced is an understatement. From Wikipedia:

British usage: Billion has meant 10^9^ in most sectors of official published writing for many years now. The UK government, the BBC, and most other broadcast or published mass media, have used the short scale in all contexts since the mid-1970s.^[12]^^[13]^^[43]^^[15]^

Before the widespread use of billion for 10^9^, UK usage generally referred to thousand million rather than milliard.^[16]^ The long scale term milliard, for 10^9^, is obsolete in British English, though its derivative, yard, is still used as slang in the London money, foreign exchange, and bond markets.

I've never actually seen the word milliard used in English outside of discussions about the long and short scale systems. However, many other languages do mainly or exclusively use long scale. For instance, my native language French.