If a search is initiated for a phrase (say red cotton kurta), will the search engine mechanism search for the full phrase or individual words?

For instance, when you type red, all the products which fall in name, category, collection, brand red will appear, when you will type red cotton, the search will become more refined, it will search for the products which have both red and cotton in common. And when you will type red cotton kurta it will make your search more specifically for a certain phrase.