Strainers are devices for getting solids out of liquid. A contrasting device is something such as a colander, which instead focusses on getting the liquid out of or off of a solid.
Sieves are devices for separating differently sized solid particles from one another: e.g. separating the coarser bran particles from wheat flour. It can loosen and aerate, such as when sifting flour before using it in baking. The act of using a sieve is called either “to sieve” or “to sift”.
Types of strainers and sieves
A chinois strainer (aka China cap) is a cone shaped strainer, used to purée soft, cooked foods for soups, stocks and sauces, coulis, and jams, etc.
A colander is a bowl with perforations in the bottom, and often sides as well. It is used for draining liquid off from food items.
A dumpling strainer is a tool for lifting a dumpling (particularly an Asian dumpling) out of the water it was simmered in.
A flour dredger looks like a large salt shaker, but it is designed for sprinkling flour. The holes in it on the top are wider than they would be for a salt shaker.
A flour duster is a tool for sprinkling flour. You can use it to dust surfaces for rolling pastry or kneading dough, dust bread dough before going into the oven, or dust baking pans.
A spider strainer is a low, shallow, round basket on a handle. It is called "spider" because it looks a bit like a metal spider web.
A tea ball is a small mesh or perforated enclosure designed to hold loose tea leaves while they are being steeped in hot water. The purpose is to provide a way to remove tea leaves all at once quickly and easily from brewed tea.
Tea strainers are small strainers used in the serving of tea made from loose dried tea leaves. The strainers are either designed to sit over the top of a tea cup, or be held there.