In SQL you need to use GETDATE():
UPDATE table SET date = GETDATE();
There is no NOW() function.
To answer your question:
In a large table, since the function is evaluated for each row, you will end up getting different values for the updated field.
So, if your requirement is to set it all to the same date I would do something like this (untested):
DECLARE @currDate DATETIME;
SET @currDate = GETDATE();
UPDATE table SET date = @currDate;