Shared Sovereignty is letting foreign powers control aspects of your government:
Shared sovereignty would involve the engagement of external actors in some of the domestic authority structures
of the target state for an indefinite period of time. Such arrangements
would be legitimated by agreements signed by recognized national authorities. National actors would use their international legal sovereignty
to enter into agreements that would compromise their Westphalian/Vattelian sovereignty with the goal of improving domestic
sovereignty. One core element of sovereignty, the ability to enter into
voluntary international agreements, would be preserved, while at the
same time another core element, the principle of autonomy, would be
The same source gives a couple of concrete examples of this, of which I have chosen one:
At the end of the
nineteenth century, shared sovereignty arrangements were created in several countries in the area of finance. The Ottoman Empire and Greece
offer two examples. The Empire entered international capital markets in
the 1850s and, after several additional loans, found itself unable to meet
its external obligations in 1875. In 1881, the Ottomans agreed to create
the Council of the Public Debt. The members of the council--one each
from Germany, Austria, Italy, and the Ottoman Empire itself, and one
from Britain and Holland together-were selected by foreign creditors.
The Council was given control over several specific sources of revenue
including the salt and tobacco monopolies, the stamp tax, and the spirits
You can see here, the Ottoman Empire gave up some of its power to foreign authorities, though retained certain privileges.
Indivisible Sovereignty, on the other hand, is almost the opposite:
As Hans J. Morgenthau once stated this point, “sovereignty over the same territory cannot reside simultaneously in two different authorities, that is, sovereignty is indivisible.”1 Sovereignty cannot be divided without ceasing to be sovereignty proper, and precisely this quality of being indivisible distinguishes sovereign authority from other forms of political power. Dividing sovereignty between two or more authorities within a given state would therefore be to dissolve that state into parts. The indivisibility of sovereignty is thus a necessary condition of the unity of the state.
So, the idea here seems to be that if you give some of your authority to someone else, you are no longer truly sovereign. Indivisible Sovereignty is the idea that two parties cannot simultaneously control a territory/population without sovereignty ceasing to exist.