Define difference between feature selection and feature reduction
Feature selection refers to deciding on what features to include in model training.

Feature reduction refers to assigning weights to features regarding how important they are for training. In linear regression, this is known as Ridge Regression (shrinking features based on L2 norm), Elastic Net, and Lasso (shrinking based on L1 norm). Lasso can shrink features to zero, so that they are effectively excluded from training (this would be similar to selection iff features are shrunken to zero).

Ridge and Lasso are very well described in the book „Introduction to Statistical Learning“. If you want to know more about Ridge/Lasso, have a look there.