I remember when I first learned the word vigintillion. It was a few hours after I learned the word viginti ("twenty") in Latin class, and I had a brain noise vigintillion and went to look up if that was a real number. Turned out, it was.
It also turned out, according to my dictionary, a vigintillion means 10^63 in the US and 10^120 in Great Britain. We both split things by powers of 1000 but we call them different things:
US system, also called the "short scale"
1,000 = thousand
1,000,000 = million
1,000,000,000 = billion
1,000,000,000,000 = trillion
1,000,000,000,000,000 = quadrillion
British system, also called the "long scale"
1,000 = thousand
1,000,000 = million
1,000,000,000 = millliard
1,000,000,000,000 = billion
1,000,000,000,000,000 = billiard
(etymologically unrelated to billiard sports, sorry)
The long scale actually makes a lot more sense, if you think about it. A billion is a million million. A trillion is a million million million.
Fortunately, since the 70s, Britain stopped using the long scale, so confusion is not actually a concern anymore; pretty much everyone uses the short scale now.
In English, at least. Many other languages, like Spanish, French, and Hungarian mostly use the long scale.
The Greeks have a strange system: they use the long scale but they don’t use the word "million". Mil means "thousand", million means "a large thousand". Now, what the Greeks use is the word called myriad. Myriad in English means "many, uncountably many, lots", but originally it means "ten thousand". So instead of million, the Greeks use "100-myriad" for million.
But the more interesting languages are the ones that don't group by thousands at all. Like Chinese and Japanese, which group by myriad (10,000).
The Chinese word for "millionaire" is 百万富翁, which breaks down to "hundred-myriad rich guy".
So the Chinese/Japanese system is
10,000 = myriad 万 (wàn, man)
100,000,000 = bimyriad 亿，億 (yì, oku)
1,000,000,000,000 = trimyriad 兆 (zhào, chou)
Yes, they still put the commas every three digits. I guess because they got those digits from the West.
Since "zhao" is so rarely used (people don't talk about quadrillions very often), it's been repurposed to the SI prefix "mega", because translating "megawatt" to "hundred-myriad-watt" is a mouthful.
And if you think having a word that means either "million" or "quadrillion" is confusing, consider that "billion" can still mean "thousand milliard" in some places.