The Gemara (Shabbat 157) establishes the foundational architecture: the halacha follows Rabbi Shimon's lenient view throughout Shabbat, except that muktzeh machmat chisaron kis — objects one guards so carefully that they are effectively set aside — is prohibited even according to Rabbi Shimon, as are objects that were muktzeh machmat issur (such as a lamp lit on that very Shabbat).
Building on this, Mishnah Berurah 308 enumerates four primary categories: (1) muktzeh machmat chisaron kis — a vessel one protects from damage; (2) muktzeh machmat gufo — objects that are neither vessels nor food, such as stones, coins, and animals; (3) a kli shemelachto le'issur — a tool whose primary use involves a prohibited labor; and (4) a permitted vessel upon which a muktzeh item rested at twilight, which remains prohibited the entire day.
Shulchan Arukh, Orach Chayim 308 rules that a kli shemelachto le'issur may be moved either for the sake of its body (le'tzorech gufo), such as using a blacksmith's hammer to crack nuts, or for the sake of its place (le'tzorech mekomo), but moving it merely to protect it from breakage or theft — meichamah le'tzel — is forbidden.
By contrast, Shulchan Arukh, Orach Chayim 308 rules that muktzeh machmat chisaron kis, such as a slaughtering knife or a scribe's penknife, may not be moved even le'tzorech gufo or le'tzorech mekomo, since the owner's stringent concern for the object effectively sets it aside entirely.
The Rambam (Mishneh Torah, Sabbath 24:12–18:1) grounds the entire rabbinic prohibition in a kal va'chomer: if the prophets warned that one's walking and speaking on Shabbat must differ from a weekday, surely the manner of carrying objects must differ as well, lest Shabbat come to resemble an ordinary day.