The Gemara in Masechet Shabbat on Daf 2, side 1, discusses one of the 39 forbidden Melachot (tasks) of Shabbat, and that is the Melacha of Hotza’ah, (of transferring). The Tosafot explains how Hotza’ah, how transferring objects from one domain to another is a forbidden task different from all the other Melachot. But in their language, this forbidden task is called a ‘Melacha Gerua’, an inferior transgression.
So let’s analyze why this task is considered inferior in comparison to all other forbidden Melachot. The Rishonim give 2 interpretations. The first is based on the fact that transferring is the only Melacha that is permissible in some areas but forbidden in others. For example, while it is forbidden to write anywhere on Shabbat, it is however permissible to carry within one’s house even though carrying outside is forbidden. This differing rule on the same item is unique and thus renders the Halacha inferior. In fact some might come, argue and challenge the restriction since transferring and carrying is acceptable indoors. The second basis for inferiority is that this Melacha of transferring or carrying is the only Melacha that is not creating or changing. All other forbidden Melachot either are creating or changing. For example, sewing, cooking and writing all are used to create. Tosafot said that this why the Masechet starts off with the laws of carrying on Shabbat. It is to show one how it important and how serious the transgression is.
There are 2 forms of carrying on Shabbat. ‘Hotza’ah’ and ‘Hachnasa’. Hotza’ah means taking something out, meaning from a private domain into a public domain. And ‘Hachnasa’ means bringing something in, meaning from a public domain to a private domain. Both are forbidden. The source of this is in the Torah and Rambam brings it down in his Halachot in Perek 12:8 in the laws of Shabbat. Moshe told the people on Shabbat not to bring any more donations for the Mishkan, and subsequently the people stopped bringing. The people listened and followed the decree as written in the Pasuk not to perform any more work, which in this case meant transferring from the private domain to the public domain. So we clearly learn from the Torah that this is a Melacha and it is forbidden on Shabbat.
What about transferring from the public domain to the private domain? The Pasuk did not write about that. So the Gemara has a simple logic, and says there is no difference in bringing in or out, and bottom line is that there is transference. So therefore, it is forbidden on Shabbat to carry from the private domain to the public domain, or public domain to the private domain.