What is the difference between a constitutional law and a law
In Britain, where I live, there isn't a distinction between constitutional law and ordinary statute law. Any law can repeal or amend any other law, and all laws follow the same procedure to be passed.
The only exception is that a law to extend the term of the House of Commons can be completely defeated in the House of Lords, rather than merely being delayed one year, as any other law could be.
Note that a law abolishing the House of Lords could be passed after the one-year delay.
Different countries put different things into their constitutions, and have different degrees of entrenchment of their constitutions. What commonalities can we draw between these? What constitutional provisions are very unusual to include? What provisions are very unusual to omit?
A constitution defines the basic framework for a government, its form and the form and relationships of its branches, the executive, the legislature and the judiciary. Furthermore most constitutions that were drafted after the French Revolution typically include a section recognizing basic human and civil rights, inspired by the Declaration of the Rights of Man and of the Citizen. Additionally constitutions often define the relationship between church and state, and in monarchies, the relationship between the monarch and state.
The main difference between constitutional and ordinary law, be it statute law, case law or convention, is that constitutional law is considered fundamental and above ordinary law in all cases. Although constitutions can be revised and/or amended the process is extremely complex1 and time consuming (and often defined in the constitution itself).
1 To get a better idea of the level of complexity, you should check out the revision and amendment processes defined in the Constitution of Greece, the Basic Law for the Federal Republic of Germany, and the Constitution of Canada.
I don't know anywhere that constitutional law can be challenged in a supreme court. The Supreme Court often gets to *interpret* the constitution, but that is not the same thing. Non-constitutional law can be challenged in court if it conflicts with the constitution, but that doesn't have to be the Supreme Court (although it usually is because something as important as that is usually appealed to the highest court).
I think Yannis alluded to this, but I would like to spell it out explicitly:
First of all, the main difference between constitutional and "normal" law is practical: the former is meant to be very hard to change, and the procedure to change it has much higher threshold than for normal laws.
This is why, for example, UK does not have what is considered a "written", or "codified", Constitution, despite having a set of laws which comprise its "Constitution". None of those laws are any different procedurally from any other law, and can be changed by the Parlament like any other law.
In contrast, most of formal constitutions have special procedures for enacting/modifying them, such as constitutional conventions, and/or special majorities needed, and/or ratification by member states (as in USA).
Second, and this one is a wee bit imprecise, a "theoretical" difference is that Constitutional law is meant to be a blueprint for how the state is organized and governed. In corporate-speak, it's a mission statement more than a specific rule. Details vary greatly, though.
As far as patterns, commonalilties and unusualness, the Wiki article on Constitution covers that in a fairly good detail. Especially "Key Features" section, listing
Entrenchment (e.g. rules for amending the Constitution itself)
Distribution of sovereignty
Separation of powers
Lines of accountability
State of Emergency rules
As far as "unusual" provisions, we have way too many to list. Some random examples:
"No person who denies the being of God, or a future state of rewards and punishments, shall hold any office in the civil department of this State." Looks like I'm not going to be working for the state of Tennessee any time soon. :-(
@SteveMelnikoff - AFAIR, Wiki indicates it is considered obsolete due to 14th Amendment of US constitution.
In Russia any law that contradicts constitution is obsolete either in full or in the contradicting part.
Also note the following. Constitution has different relations to international treaties than other laws.
Constitution has priority over ratified international treaties, while at the same time the treaties have priority over other laws.
This made so out of the following considerations: the state cannot unilaterally change their laws so to nullify or contradict the treaties it has concluded. Otherwise it would be easy to go out of the treaties by just unilaterally changing the national law. On the other hand, all the treaties should abide the constitution. In other words, treaties are not allowed to damage fundamental rights of the people, the system of government and the sovereignty of the nation.