Punjab is a state within the Indian Union but it is not sovereign. It has no separate entity in foreign relations. A state is one which has Population, Territory, Government and Sovereignty.
Although Punjab possesses the first three attributes it lacks the fourth one. Hence it is not a sovereign state.
Pakistan is a sovereign state. It is a republic. It is a member of the Commonwealth of Nations as India is. All the members of Commonwealth are sovereign states whether they are dominions or Republics.
They are equal and have the discretion to leave the Commonwealth at their will. Of course, the Queen of Britain is the head of Commonwealth but she is only symbolic head.
Other heads of states of the Commonwealth countries enjoy equal status. This symbolic headship in no way infringes upon the status and position of these heads. Membership of the Commonwealth is in no way a bar on the sovereignty of its members.
It is not a sovereign state. It is an international organization. It possesses its own personality and has its character and various organizations. The General Assembly is the highest organ and may be compared to Legislature in a state. The Security Council is like the Executive.
It has the International Court of Justice as its Judicial organ. Besides it has economic and cultural organizations like the Economic and Social Council, the Trusteeship Council, the UNESCO, etc. Sovereign states can alone become its members. But the U.N.O. is not a sovereign state.
Its officials enjoy diplomatic immunities as the diplomatic representatives of states do, yet it is not a state. It has no population of its own, nor territory. Nor it exercises sovereignty as states do. It has little jurisdiction upon non-number states thus U.N.O. is not a state.