They don't, Easter Saturday is the Saturday following Easter. Holy Saturday is the day before Easter.
The name of the Saturday before Easter is called Holy Saturday.
Holy Saturday is part of the Easter season.
Easter Saturday is the Saturday after Easter Sunday. It is not, as many people think, the Saturday before Easter Sunday. That is Holy Saturday. It may be Holy Saturday that you are asking about though. Saturday is the Jewish Sabbath, so no work could be done. So very little and nothing of significance happened on Holy Saturday. As it was a day of rest, that's why there was such a rush to get the body of Jesus entombed before sunset on Friday and why Jesus lay in the tomb on Holy Saturday, waiting until Sunday to rise and why the ladies didn't go to prepare the body of Jesus until the first day of the week, which is Sunday. They found he had risen and much later Christians adopted Sunday as their Sabbath in honour of the Resurrection.
Holy Saturday
For Christians there is an Easter Saturday although it is not as dramatic as Sunday or Friday. Friday is when Jesus died on the cross. Saturday is when Jesus was placed in the tomb and Sunday is when Jesus resurrected and went back to Heaven.
The day before Easter is called Holy Saturday.
Holy Saturday
Morning Prayer ( Liturgy of the Hours). There is no Mass on Holy Saturday, before the Easter Vigil.
Roman Catholic AnswerThe Easter Triduum.
It is not sung on Holy Saturday until the Easter Vigil Mass that evening;then it is sung after the reading of the Epistle
Black Saturday sometimes is used to refer to Holy Saturday, the day before Easter Sunday. It is rarely used, at least, in the United States.
The Easter Season begins at or near the midnight between Holy Saturday and Easter Sunday, with the celebration of the first part of the Divine Office (liturgical prayer-cycle) of Easter Sunday. This normally takes place during the celebration of the first Mass of Easter commencing near midnight on the night of Holy Saturday. In various places for various reasons, the first Mass of Easter might be held some time during the earlier evening of Holy Saturday. In the concluding part of the first Mass of Easter, the first part of Easter Divine Office is celebrated and this is (strictly speaking) when the Easter Season begins. Before certain changes in the 1950s, the Easter Vigil was celebrated in the morning hours of Holy Saturday, and the Easter Season commenced when the vigil ceremonies has been completed (that is, in the afternoon of Holy Saturday). Since the 1950s, the rule is that the Lenten fast continues until the midnight between Holy Saturday and Easter Sunday. Obviously, if people are taking part in the Easter Vigil ceremonies, they will not be eating or drinking (except for taking water or medicines in an emergency), and so the Lenten fast is observed for the entire day, and the Easter Season commences at or near the midnight.