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
Sometimes z-score refers to a quantile randomized z-score, where the quantiles of distribution are mapped to z of a standard normal, so by construction, z-score of one is bigger than 68.27% percent of values in the distribution, regardless of how many standard deviations from a mean a value is.
