Use "billion" rather than "thousand million" if you are writing or talking in English to people in the U.K., U.S., Australia, or Canada.
When you are reading, be aware:
"Thousand millions of" is old-fashioned and no longer used. It was correct in the 1800s and you will read it in books from that era. (For example, in a speech, Abraham Lincoln used the phrase "two thousand millions of dollars.") Don't use it.
The word "billion" is a cultural and historical puzzle. Sometimes it means a thousand million, 1,000,000,000. Sometimes it means a million million, 1,000,000,000,000. When I was a kid, it meant 1,000,000,000 in the United States and 1,000,000,000,000 in the U.K. Therefore, at that time, the British used the phrase "thousand million."
The British have now switched to using "billion" to mean 1,000,000,000.
When you are reading and see the word "billion," be aware that it can mean either of two different numbers. Look for context to be sure you know what the writer means.
You can use "thousand million" and it will be understood. It has the advantage of being unambiguous, particularly if you are writing for a truly international audience. "Billion" is more natural.
If you love this kind of topic (Canadians use "billion" differently depending on whether they are speaking English or French, for example), see the incredibly long Wikipedia article, "Long and short scales," https://en.wikipedia.org/wiki/Long_and_short_scales
for the unbelievably complicated story.