A cooking sieve is a type of strainer or separator. You use a cooking sieve when you want to separate seeds from juices or leaves from tea or just to push something through to change the consistency like a cheesecloth would do.

A sieve or often called a sifter is a kitchen utensil that is used to remove unwanted materials from the source or is often used to air-rate and remove lumps from flour, and often used to drain pasta from its water etc.