Friday in Arabic is Jumu'ah. Sabbath is a Jewish holy day of rest from Friday evening to Saturday evening and the Christian holy day of rest is on Sunday. They are both on different days and different events. Jumu'ah is the best day as many virtues are bestowed on this day.
It was narrated that Abu Hurayrah and Hudhayfah (may Allaah be pleased with them) said:
The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Allaah led those who came before us away from Friday. The Jews had Saturday, and the Christians had Sunday. Then Allaah brought us and Allaah guided us to Friday. So there is Friday, Saturday and Sunday, and thus they will follow us on the Day of Resurrection. We are the last of the people of this world but we will be the first on the Day of Resurrection, and we will be dealt with before all others.”
Narrated by Muslim, 856.
It was narrated from Aws ibn Aws that the Prophet (peace and blessings of Allaah be upon him) said:
“The best of your days is Friday. On that day Adam (peace be upon him) was created; on that day he died; on that day the Trumpet will be blown and on that day all of creation will swoon. So send a great deal of blessings upon me, for your blessings will be shown to me.” They said, “O Messenger of Allaah, how will our blessings upon you be shown to you when you have turned to dust?” He said, “Allaah has forbidden the earth to consume the bodies of the Prophets, peace be upon them.”
Narrated by Abu Dawood, 1047; classed as saheeh by Ibn al-Qayyim in his comments on Sunan Abi Dawood, 4/273; classed as saheeh by al-Albaani in Saheeh Abi Dawood, 925.
These hadiths clearly explain the significance of Jumu'ah and how the day is much more important than any other day. In the first hadith it says why Jews celebrate Sabbath on Saturday and why Christians celebrate it on Sunday.
Calling Jumu'ah (the blessed day) 'Sabbath' is imitating the kuffaar and the Prophet forbade to imitate the kuffaar. It is supposed to be separate from the disbelievers.
Allah knows best.