The decimal system, which we are familiar with, uses a base of 10 digits (0 to 9). The number of digits before you "add another digit" is also called the radix.

The sexagesimal system, or base 60, was used by the ancient Sumerians around 5000 years ago. The usefulness of a base 60 system comes from how many factors go into 60, and therefore how much it can be subdivided into integers.

I'm not sure about any confusion in history because of conflicting base systems, other than that if you don't convert from one system to another correctly you'll get a different number. Also, the Sumerian base 60 system did not have a zero, and so some context was needed to evaluate some written numbers.