All the different categories of Muktzah are certainly confusing! What is even more interesting is that fact that the Halachah is with Rebbi Shimon -- who argues with Rebbi Yehudah and holds "there is no Muktzah!" That is, with certain exceptions.... (See Mishnah Berurah beginning of Siman 308, for a nice intro to the laws of Muktzah.)

In general, Muktzah always means set aside *not* to be used for a particular use. Concerning Shabbos, it was set aside not to be used on Shabbos. Nevertheless, as you say, sometimes it was set aside for *other* use (such as Huktzah L'Mitzvaso -- something that is "set aside" to be used for a decorating a Sukah etc., and not to be used for normal use, Shabbos 45a).

Muktzah Machmas Isur means that it was not meant to be used *due to* (Machmas) an Isur. In our case, there is an Isur of slaughtering an animal on Shabbos. Because of this, one does not plan to eat an animal that is alive upon the start of the Shabbos for the duration of the Shabbos. The Gemara suggests (top of 15a) that this Muktzah may be limited to objects that the person *made* unfit for Shabbos (such as a candle that the person lit before Shabbos and was still burning when Shabbos started). It does not apply to an animal that just *happens* to be unfit, because it is alive. (The Rishonim point out that Halachically, this is of course not accepted. See Insights to Daf 15:4).

Muktzah Machmas Mi'us means that an object was not intended to be used for the duration of the Shabbos *due to* its repulsive state in the beginning of the Shabbos. One does not normally re-use a used lamp of Cheres, since it looks disgusting after being used. Rebbi Yehudah makes it Muktzah for the duration of the Shabbos since it was "set aside" not to be used, due to its repulsive state, at the start of the Shabbos.