Read what each search engine has to say about "Advanced search" methods.

Usually a keyphrase in quotes return results for exactly that keyphrase with the key words in that exact order. Not using quotes mix and mashes the words in various orders; usually resulting in more web pages being offered in the SERPs.

Using quotation marks creates better search precision.

so lets say that "big widget" comes in at position 20 with quotes and position 40 without quotes, would that mean that i should try and remove the words big and widget from the page where they are not together to increase my web position?