A calculated column is just like any other column in a table defined by a DAX expression and is evaluated on a row-by-row basis. A calculated column can also be used to define a relationship if required. However, a calculated column always uses RAM and wastes valuable space.
Measures are another way of calculating using DAX expression. Measures are mostly used whenever you want to aggregate values such as SUM, AVERAGE, MIN, MAX, and COUNT.
At any time if you operate on aggregate values rather than on a row by row basis, measures have to be created.
The main difference between the calculated column and measures is the context of evaluation.
A measure is evaluated on aggregations of data defined by the current context of the cell of the pivot table or DAX query
Whereas a calculated column is computed at the row level of the table and uses the current row as a context, it does not depend on the user activity on the pivot table.