Variance measures how much an element deviates away from the mean. Dependent T-tests are useful when you are analyzing data involving 1 independent var. For example, comparing IQ by ethnic group. For example, comparing IQ by ethnic group AND gender. These tests are used to determine whether a relationship exists between two quantifiable variables.
Correlation simply means that a relationship of some kind exists between two variables.
For example, investigating the relationship between IQ and gender may reveal a correlation, using certain types of tests, between IQ demonstration and gender. There are both Parametric and NonParametric types of tests for data. Correlations may be described as either Positive or Negative. For example, increasing the amount of guided study yielding increased scores on objective-type tests would be a positive correlation. Decreasing the amount of guided study yielding corresponding decreased scores on objective-type tests would ALSO be a positive correlation.