Find * and Omit = (no need for two = in this case) will produce identical results in many, but not all uses.
* requires that there be at least one character in the field. = with no added characters finds all records where the field is empty. Omit them and you again get all records where there is at least one record in the field.
If the field in which you are entering this search criteria is from a related table. This has two affects on your results:
1) If the related table is from the "many" side of a one to many relationship, any related record that matches your search criteria will result in FileMaker finding the layout's parent record linked to it. This can produce what appears to be inconsistent results as the data from the record that was responsible for the layout record being found may not even be visible on your layout in some cases.
2) If there is no related record, = will not find that record as this is looking for records where the field is empty, not cases where the record does not exist.