The second half of Sefer Shemos deals almost exclusively with the construction of the Mishkan, excluding the interlude of the cheit haeigel. Although physically the construction described in Vayakheil Pekudei followed precisely the commands in Terumahand Tetzaveh, there was a fundamental distinction between the original plan of the Mishkan and its actual implementation.
Following the order of the pesukim, the mitzvah of building he mishkan preceeded the cheit haeigel, whereas the construction followed the cheit. A mishkan built after the cheit was different in nature than one that would have been built before the cheit. The area of the mishkan endowed with the highest level of kedusha was the kodesh hakodashim, which housed the aron containing the luchos. While the aseres hadibros appeared on both the first and second luchos both, the essence of the two sets was different. The first set is described as "v'haluchos maaseh Elokim - the work of Hashem", whereas the second set was carved out by Moshe Rabbeinu, with only the letters being carved out by Hashem.
This distinction was reflected in the nature of the kedushas mishkan. The "first" mishkan that would have been built if not for the cheit would have housed the luchos of "maaseh Elokim". The kedusha would have emanated from Hashem. The "Second" mishkan that actually was built required human participation and its kedusha was initiated by Bnei Yisroel and it only subsequently received the blessing from Above. After all the human input, Moshe Rabbeinu could only pray that "yehi ratzon shetishre shechina b'maase yedichem - let the divine presence rest upon your work" (Rashi Shemos 39:43). This mishkan was not "maaseh yedei hashem", but rather "maaseh yedeichem". The luchos of "maaseh Elokim" had been transformed into the luchod of "psol lecha" - stones carved by a human being that would be written upon by Hashem.
Two distinct types of sanctity, one stemming from Hashem and the other indicated by man, is a common theme in halacha. Shabbos receives it sanctity directly from hashem, while yom tov requires the Jewish people to endow it with holiness by declaring the news moon. This halachic distinction is reflected by the text of the berachos "mekadesh haShabbos" and "mekadesh Yisroel vehazemanim"; Hashem sanctifies Shabbos while the Jewish people sanctify the yomim tovim (gemara Pesachim 117b). Similarly, there is a distinction between the sanctities of Eretz Yisroel and of Yerushalayim. The Rambam (Hilchos Beis Habechira 6:16) explains that kedushas Eretz Yisroel with respect to the agricultural mitzvos can be revoked because its kedusha emanates from being possessed by Bnei Yisroel. Therefore, in their absence, the kedushas haaretz is lost. This is in contrast to the kedusha of Yerushalayim with respect to korbanos which can never be lost, because its kedusha is derived directly from Hashem, who is eternal.
These two models of mishkan materialized in the two batei mikdashos. The first Beis Hamikdash resembled the original plan for the mishkan - present were the shechina, the urim vetumim, and prophecy. It had all the qualities of "maaseh Elokim - the work of Hashem". On the other hand, the second Beis Hamikdash, devoid of the urim vetumim and nevuah, was built by the Jewish people and endowed with sanctity through human effort and fervent prayer that the shechina rest upon it to some degree.
Each of the two batei mikdashos had a unique downfall which undermined its source of holiness. The Beis Hamikdash of "maaseh Elokim", whose sanctity stemmed directly from the shechina, could not conceivably last in the presence of idolatry, just as the avodah zarah of the cheit haeigel destroyed the plans to construct a mishkan which would house the luchos that were carved by Hashem.
The destruction of the second Beis Hamikdash was precipitated by divisiveness within the Jewish people, characterized by sinas chinam - baseless hatred. A Beis Hamikdash that owed its existence and sanctity to the Jewish people can only exist when the Jewish people are united, not when they are split by baseless hatred. Our ability to create kedushas hamikdash is conditional on our acting as a united people.
As we begin chodesh Nissan, may we merit to be redeemed as in the days of Yetzias Mitzrayim, and once again see the Beis Hamikdash and be privileged to serve Hashem as in the days of old.