active record: design pattern for relational databases. It allows us to retrieve and manipulate data as objects rather than static rows.
ActiveRecord: Rails implementation of active record pattern. It not only contains data from table rows but also methods for CRUD operations on rows. With ActiveRecord we can manipulate data from database and save them back.
ActiveRelation or ARel: Object-Oriented interpretation of relational algebra. It simplifies the generation of complex database queries, allows us to create small chainable database queries, helps in creating complex joins and aggregations using efficient SQL etc.