... are both specialised types of rest, used when access to the cue ball is obstructed by other balls. The spider gives a higher fulcrum for the cue; the swan (also, and probably more correctly, known as the swan neck) has an extension which places the fulcrum above the obstructing balls, and is used in more extreme cases.
These rests may occasionally be used in billiards, but less frequently because there are far fewer balls on the table. Also in pool, but in this case the balls are usually more spread out so a major obstruction is less likely.
I apologise if there are any other sports where spiders and swans are used. I couldn't think of any, but that doesn't mean there aren't any.
© Haydn Thompson 2022