Can Z values be thought of as the number of standard deviations? I read about the 68-95-99.7 rule that shows

I also read that a Z value of 1.96 gives a confidence level of 95%
Is it correct to think of Z as the "number of standard deviations" ?
Only I have never seen it mentioned that way.

No. The z score is not 'the number of standard deviations'. Instead the z-score of a value is the number of standard deviations that value is above the mean. A z-score of 1.7 is 1.7 standard deviations above the mean. A z score of -1 is one standard deviation below the mean, and so on.
This is not mere nitpicking, it's essential to correctly conveying your meaning. I have seen exactly this imprecision in relation to z-scores lead to error on numerous occasion. Stats is not the place for woolly thinking and muddled words $-$ it is tricky enough when you say exactly what you mean.
