With calculated columns, you can add new data to a table already in your model. But instead of querying and loading values into your new column from a data source, you create a Data Analysis Expressions (DAX) formula that defines the column's values.
Measures are created and used in Report View or Data View. Measures you create yourself appear in the Fields list with a calculator icon. You can name measures whatever you want, and add them to a new or existing visualization just like any other field.