two apparently equal calculated measures are actually different

When you define a variable with VAR, that value is treated as a constant when referenced later.

Therefore, in your first measure, var2 is the same as var1 since a constant is not changed by adjusting the filter context with CALCULATE.

If instead of defining a temporary variable, you defined var1 as a separate measure, then it would function as you expected it to in your first example.

As a side note, you can use multiple conditions rather than nesting CALCULATE functions:

measure3 =
CALCULATE (
    [measure],
    table[column_1] = "some value in column 1",
    table[column_2] = "some value in column 2"
)