Cue sport are also known as billiard sport 
Cue sport is a type of billiards?
Yes. Historically, the umbrella team was billiards 
Can you explain what the umbrella team is?
Cue sports
Cue sports (sometimes written cuesports), also known as billiard sports, 
are a wide variety of games of skill generally played with a cue stick, which is used to strike billiard balls and thereby cause them to move around a cloth-covered billiards table bounded by elastic bumpers known as .
Historically, the umbrella term was billiards. While that familiar name is still employed by some as a generic label for all such games, the word's usage has splintered into more exclusive competing meanings in various
Glossary of cue sports terms
The following is a glossary of traditional English-language terms used in the three overarching cue sports disciplines: "carom (or carambole) billiards" referring to the various games played on a billiard table without ; "pool", which denotes a host of games played on a table with six pockets; and "snooker", played on a large pocket table, and which has a sport culture unto itself distinct from pool. There are also hybrid pocket/carom games such as English billiards