Criterion-related validity
This examines the ability of the measure to predict a variable that is designated as a criterion. A criterion may well be an externally-defined 'gold standard'. Achieving this level of validity thus makes results more credible.
Criterion-related validity is related to external validity.
Predictive validity
This measures the extent to which a future level of a variable can be predicted from a current measurement. This includes correlation with measurements made with different instruments.
For example, a political poll intends to measure future voting intent.
College entry tests should have a high predictive validity with regard to final exam results.
Concurrent validity
This measures the relationship between measures made with existing tests. The existing tests is thus the criterion.
For example a measure of creativity should correlate with existing measures of creativity.