The pasuk refers to the stopping of time by the sun standing in place as the "silence" of the sun. Rashi offers a very insightful interpretation as to why the term "silence" is appropriate.
וידום - שתק מלומר שירה, שבכל עת לכתו אינו שותק, ובעמידתו שותק, ויהושע אומר שירה בשבילה דכתיב אז ידבר יהושע
Rashi explains that as the sun travels it sings, but the song of Yehoshua filled in for the sun to allow it to remain silent - to stand in place. What does this mean?
The concept of "shira" - song, is the fulfillment of the command of Hashem, confirming him as the creator and conductor of the world. As the sun travels from its rising to its setting, it is following the laws of nature set by Hashem, thereby publicly sanctifying the name of Hashem. "Shira" is the public kiddush Hashem - sanctification of Hashem's name. The sun cannot stop because there would be a necessary Kiddush Hashem missing in the world. However, when Yehoshua sings "shira" and publicly recognizes the hand of Hashem in the battles that he is fighting, the Kiddush Hashem of Yehoshua can replace that of the sun, thereby enabling the sun to stand still, in silence. Perhaps this will answer the question of Tosafos from Yaacov Avinu. The fact that the sun will rise early or set more quickly doesn't constitute a silence since it is still moving the entire time whether quickly or slowly. It is only when the sun literally stands still - ויעמוד השמש בחצי השמים ולא אץ לבא that there is a lack of "shira" which must be compensated for. That would also explain why by Chizkiyahu Tosafos writes that the sun went backwards, but couldn't stand in silence, unless there was a kiddush hashem of a major caliber to compensate for it.