The prohibition of carrying on Shabbos is fundamentally different that the first thirty-eight melachos that one cannot do on Shabbos. Although all of the thirty nine melachos were done in the construction of the mishkan and are derived from the juxtaposition of Shabbos and mishkan, Chazal derive the prohibition of carrying from a separate source. In parshas Vayakhel Moshe instructs the Jewish people to stop bringing materials for the mishkan. Chazal in maseches Shabbos (96b) interpret this event as referring to Shabbos. They were told not to carry materials on Shabbos, thereby teaching us that carrying is forbidden on Shabbos. Tosafos in maseches Shabbos (2a) question the necessity for an explicit prohibition against carrying. If carrying was involved in the process of constructing the mishkan, it should be included in the definition of melacha which includes all mishkan oriented activities. Just as there is no distinct source to prohibit the other melachos, so too carrying should not require its own prohibition.
Tosafos answers that carrying is a "melacha geruah" - an inferior category of melacha. If not for its distinct source of prohibition, it would have been permissible notwithstanding its role in the construction of the mishkan. What is inferior about carrying that differentiates it from other melachos? The other melachos involve a physical change in the object. Actions such as cooking, lighting a fire and writing cause a physical change, whereas an item that is carried remains the same. If carrying is so different than the other melachos, why does the Torah prohibit it? If Shabbos is the commemoration of Hashem resting from creation, it is understandable that we refrain from "creating" by changing physical objects. Why should carrying be included in this commemoration if it is not an act of creation?
When Yosef is appointed as the second in command to Pharoh (Braishis 41:44), he is told that no one will lift up a hand or foot in Mitzrayim without his permission. These words define what an absolute ruler is. One cannot lift an object or walk without the permission of the king.
Shabbos observance is the expression of the acceptance of Hashem as Creator and King. The other thirty-eight melachos declare Hashem is the Creator and the melacha of carrying declares Hashem is the King. One does not lift an object and carry it without the permission of the King.
Perhaps it is this connection between Hashem the King and carrying on Shabbos that prompted Chazal to institute an otherwise very difficult halacha to understand. The Gemara (Rosh Hashana 29b) tells us that we do not blow the shofar when Rosh Hashana falls out on Shabbos. Chazal were concerned that someone may forget it is Shabbos and carry the shofar. Given that the mitzvah of shofar is an essential aspect of Rosh Hashana, how can Chazal say that the remote possibility that someone may carry the shofar outweighs the entire Jewish people not hearing the shofar? The primary theme of Rosh Hashana is the accepting of Hashem as our King. The shofar is blown just as trumpets are sounded at a coronation. The shofar itself being carried on Shabbos would be the greatest contradiction to the kingship of Hashem. To lift up an item the King Himself prohibits and use it for His coronation is inconceivable. When Rosh Hashana falls out on Shabbos, we coronate Hashem in a very different way. Rather than blowing the shofar, we strengthen our observance of the melacha of carrying, thereby accepting Hashem as our King in the true spirit of Rosh Hashana.
Of all the thirty nine melachos, the halachos of carrying are given the most attention by Chazal. In addition to many sugyas in maseches Shabbos almost the entire maseches Eruvin deals with the complexities of this melacha. The numerous prohibitions instituted by Chazal to safeguard this melacha date back to Shlomo Hamelech (Eruvin 21b). Such care is given not to violate this melacha. Although it is technically a "melacha geruah - an inferior melacha" - its message is central to Shabbos. The proper observance of its intricate details is our expression of kabolas ol malchus shomayim. May we merit to study the laws of Shabbos and observe it properly, thereby declaring that Hashem is our Creator and King.