This is the push-your-luck family. You roll six dice, set aside the ones that score and face the same question every turn: bank the points, or roll again and risk losing them all. Farkle is the best known name, Ten Thousand the classic target-score version.
Roll six dice, set the scoring ones aside and stop before an empty roll takes the whole turn.
Roll six dice, set scoring dice aside and stop before a farkle wipes out your turn.
The same tension powers simpler games. In Pig one die and one bad roll can wipe your turn, and Drop Dead kills your dice one by one. They make good warm-ups before a full evening of Farkle.
No two families play these games quite the same way. The pages here describe the common core and mark the popular variants, so you can agree on a table before the first roll instead of arguing after it.