There is a positive mitzva to refrain from melakha on Yom Kippur, as we read, “It shall be a Shabbat of complete rest for you” (Vayikra 23:32). If one works on Yom Kippur, not only is he not fulfilling the positive mitzva to desist from melakha, but he is also violating the negative mitzva, “You shall do no melakha throughout that day” (ibid. 23:28). Since Yom Kippur is referred to as Shabbat, the thirty-nine categories of melakha prohibited on Shabbat are also prohibited on Yom Kippur. It is only regarding punishment that there is a difference between Yom Kippur and Shabbat. While someone who knowingly undertakes melakha (in the presence of witnesses after being duly warned) is subject to stoning on Shabbat, he is subject to karet on Yom Kippur. (One who unknowingly does melakha on either day must offer a sin offering.) Thus we read (ibid. v. 30), “And whoever does any melakha throughout that day, I will cause that person to perish from among his people” (MT, Laws of Resting on the Tenth 1:1-2; SA 611:2).
As on Shabbat, the mitzva to rest on Yom Kippur includes an obligation not to treat it as a weekday. That is, in addition to refraining from melakha, one is meant to refrain from doing burdensome activities. One must not open a store or move heavy items in preparation for weekday activities. Even though one who does so is not engaging in one of the thirty-nine melakhot, he is negating the mitzva to rest on Yom Kippur, as it is written, “It shall be a Shabbat of complete rest for you” (Vayikra 23:32). The mitzva is to preserve the sanctity and character of the day. One’s entire demeanor is meant to be different than on a weekday (Peninei Halakha: Shabbat 22:1). In general, all laws of Shabbat apply to Yom Kippur, and there is the additional mitzva of fasting on Yom Kippur, so it involves a more complete withdrawal from mundane affairs.