Personally, I don’t like the word “volatility” at all.
It is really a correlation to how the stock moves with respect to the market. The .66 may be a result of the fact that lately, Apple has been moving downward while the market moves up so it appears somewhat disassociated with the market.
Look at how it is derived. Calculate the beta for a couple of stocks and you’ll understand better what it means.
A correlation of 0 means you can’t infer what the stock might have done by looking at the market index. I believe you could have two different securities, each with a beta of zero, each with very different volatility.