The term 'chaos'
seems to have appeared about the same time as the first uses of digital
computing to integrate differential equations that are not analytically
solvable. While it is true that many of these display very strange behavior,
the behavior is still deterministic, not random. The imperfections
in our attempts to integrate them are the source of the 'chaos'!
An exact set of initial conditions completely determines the motion
that follows the starting time. The motion is predictable, NOT random.
The real chaos appears because we have to try to represent the Math using digital computers. Our computers represent a number, any number, using a finite number of digits. But real numbers contain an infinite number of digits. Therefore all computer numbers are just approximations to actual values. This is actual source of the randomness in 'chaos'!
The reason I don't like the term 'chaos' is that it seems that it was invented to put a new name to an old subject (non-linear differential equations). When high speed computing became possible, the people who applied it to these equations wanted a new, flashy term for the the subject to convince other people that they were actually doing something radically original and revolutionary...