Z score: the basic standard score
A Z score tells you how far a value is from the average, measured in standard deviations. A Z score of 0 is exactly at the mean. A Z score of 1 is one standard deviation above the mean, and -1 is one standard deviation below it. This makes scores from different tests easier to compare when the groups have different averages or spreads.
T score: the same idea on an easier scale
A T score is often calculated as T = 50 + 10z. It keeps the comparison meaning of the Z score but avoids many negative values and decimals. For example, z = 1 becomes T = 60, and z = -0.5 becomes T = 45. This is why T scores are common in test reports and selection workflows: they are easier to read while still being based on the group distribution.
PR and percentile: position in the group
Percentile rank answers a different question: approximately what share of the group scored below this score? A PR of 80 means the score is above about 80% of the comparison group, not that the person got 80% correct. It is useful for explaining relative position, but it depends heavily on the actual group and method used to calculate it.