A Z-test is similar to a t-test. In both cases, the central tendency of a normally distributed sample is compared with either a fixed value or the value of another group. Read more about the differences between z and t tests.
Z-scores indicate the difference between the observed distribution and the comparison in standard deviation units. Z-scores derive from the properties of a normal distribution, e.g., 95% of scores will be less than a standardised z-score of 1.96.