Classification problems are mainly used when the output is the categorical variable (Discrete) whereas Regression Techniques are used when the output variable is Continuous variable.
In the Regression algorithm, we attempt to estimate the mapping function (f) from input variables (x) to numerical (continuous) output variable (y).
For example, Linear regression, Support Vector Machine (SVM) and Regression trees.
In the Classification algorithm, we attempt to estimate the mapping function (f) from the input variable (x) to the discrete or categorical output variable (y).
For example, Logistic Regression, naïve Bayes, Decision Trees & K nearest neighbours.
Both Classifications, as well as Regression techniques, are Supervised Machine Learning Algorithms.