Hello, @Crogers,
Ajax search in header delivers users instant and changing results as they type in the dropdown which shows the product. That’s why you see different result till the moment when the full word is entered. We’ll add the option to disable predictive search in next theme update if you don’t like it.
By default, it searches by title and description (in the same way as WooCommerce Search widget works). If you need more advanced search (by sku, by title only) I would recommend you to use additional plugins.
Regards