RESUME 
CROSS APPLY - Similar to INNER JOIN
OUTER APPLY - Similar to LEFT JOIN
 
 SQL Server APPLY operator has two variants; CROSS APPLY and OUTER APPLY
The CROSS APPLY operator returns only those rows from the left table expression (in its final output) if it matches with the right table expression. In other words, the right table expression returns rows for the left table expression match only.
The OUTER APPLY operator returns all the rows from the left table expression irrespective of its match with the right table expression. For those rows for which there are no corresponding matches in the right table expression, it contains NULL values in columns of the right table expression.
So you might conclude, the CROSS APPLY is equivalent to an INNER JOIN (or to be more precise its like a CROSS JOIN with a correlated sub-query) with an implicit join condition of 1=1 whereas the OUTER APPLY is equivalent to a LEFT OUTER JOIN.
 
Using APPLY
Both the left and right operands of the APPLY operator are table expressions. The main difference between these operands is that the right_table_source can use a table-valued function that takes a column from the left_table_source as one of the arguments of the function. The left_table_source can include table-valued functions, but it cannot contain arguments that are columns from the right_table_source.

The APPLY operator works in the following way to produce the table source for the FROM clause:

Evaluates right_table_source against each row of the left_table_source to produce rowsets.

The values in the right_table_source depend on left_table_source. right_table_source can be represented approximately this way: TVF(left_table_source.row), where TVF is a table-valued function.

Combines the result sets that are produced for each row in the evaluation of right_table_source with the left_table_source by performing a UNION ALL operation.

The list of columns produced by the result of the APPLY operator is the set of columns from the left_table_source that is combined with the list of columns from the right_table_source.