The Sages forbade moving things that are not fit for use on Shabbat or Yom Tov, and that one therefore puts out of his mind (maktzeh mi-da’ato). There are two fundamental reasons for this prohibition: 1) To preserve the atmosphere of these holy times as days of rest dedicated to holiness and peacefulness. The idea of rest applies to one’s hands as well; they should not move objects or be involved with activities that are not connected to Shabbat or Yom Tov. If moving items unnecessary for these holy days were permitted, people might well spend the whole time cleaning and arranging their homes and belongings, thus negating the mitzva to rest. 2) To set up a safeguard so that one will not come to do melakha on Shabbat or Yom Tov, for if one carries an unnecessary item on Yom Tov, there is a concern that he will use it to do a forbidden melakha or that he will end up carrying it from one domain to another. As we have seen, one who carries an unnecessary item transgresses a Torah prohibition (section 3 and n. 2 above, in accordance with the majority of poskim).
As a general rule, muktzeh prohibitions on Shabbat and Yom Tov are the same, so it is unnecessary to repeat the laws which are already spelled out in Peninei Halakha: Shabbat (ch. 23). However, there are three areas in which there are differences between the two days. In two of the areas, Yom Tov laws are more lenient than those of Shabbat, while in one area, they are more stringent than those of Shabbat.
The first difference is that on Shabbat, some food items are muktzeh because they cannot be eaten in their current state. These include flour, raw chicken, raw meat, and raw potatoes (Peninei Halakha: Shabbat 23:3). In contrast, on Yom Tov cooking is permitted, so these items are not muktzeh. Some objects are muktzeh on Shabbat because they are used in food preparation, such as burners and pots (ibid. 23:7-8). These items are not muktzeh on Yom Tov because cooking is permitted. Similarly, desk lamps and electrical appliances with a heating element or incandescent filament are muktzeh meḥamat gufam on Shabbat because they contain fire, which may not be lit on Shabbat (ibid. 23:7). On Yom Tov, however, these appliances are not muktzeh because one may transfer a flame then (SSK 13:46).
The second difference is that on Yom Tov, all types of muktzeh may be moved le-tzorekh okhel nefesh. For example, if plaster fell into an oven, it may be removed so that the food for the Yom Tov meal is not charred, even though the plaster is muktzeh (SA 507:4; Rema 509:7; 518:3). Similarly, let us say there are rocks resting on top of fruit. Since the rocks are muktzeh, they may not be moved on Shabbat even if one wishes to take the fruit (although he may use his leg or any body part other than his hands, to take them). In contrast, on Yom Tov the rocks may be moved. Just as the Sages permitted melakha le-tzorekh okhel nefesh, so too they permitted moving muktzeh rocks to enable people to eat the fruit (MB 509:31; 518:23). If a key that would allow access to food is in a purse, on Shabbat it may not be removed, since the purse is muktzeh. In contrast, on Yom Tov the purse may be opened and the key removed, because the purse is being moved le-tzorekh okhel nefesh (MB 518:24). However, if a different key is readily available, and using it would avoid the need to move muktzeh, the alternative key should be used.
This entire leniency is limited to cases in which the muktzeh is being moved in order to access items that are necessary for food preparation. In contrast, it is forbidden to eat or use items that are themselves muktzeh. For example, one may not eat fruit that a non-Jew picked on Yom Tov or fish or fowl that a non-Jew caught on Yom Tov. Since it is forbidden for a Jew to pick fruit or trap animals on Yom Tov, we assume that he had put them out of his mind (SA 515:1; MB ad loc. 5). Similarly, valuable wood designated for construction may not be used to fuel a fire for cooking on Yom Tov, since it is muktzeh meḥamat ḥesron kis (SA 502:3).