Unpaired t-test Can be used to compare two random samples provided they both follow a normal distribution. Samples can be of differing size but should be independent ie. If some of the measurements were made in the same subjects then can be corrected for repeated measures . Regression and Correlation Regression indicates a mathematical relationship between two or more variables. Parametric analysis rules apply so data must either be normally distributed or can be converted into something with a normal distribution eg.
Correlation indicates an association between two variables.
Non-parametric rules apply as the association is calculated between the ranks of the variables, not the variables themselves eg. ASA v mortality rate. A correlation describes an association . Not cause and effect . In medicine we frequently want to compare two different methods of measuring the same variable eg. invasive and non-invasive blood pressure.