There are many different constitutions. Some are short and deal with only the most basic points for governing a country - others are long and very detailed. The MindMap below (click on it to increase its size) highlights some of the key ways of distinguishing constitutions.
The first is Written/Unwritten - a misnomer because most constitutional rules are written down in one place or another. The term "Written Constitution" applies to ones where there is a single document setting out the rules. However, don't be fooled - it may have supplementary sources which define and explain it. For example you couldn't fully understand or apply the US Constitution without referring to caselaw; more detailed laws putting the flesh on the Constitution; and relevant commentaries. The UK Constitution is not found in a single document - but in statute (Magna Carta 1215 - yes a statute! and a tiny bit still remains in the original source; Bill of Rights 1689; Act of Settlement 1701...European Communities Act 1972; Human Rights Act 1998; Constitutional Reform Act 2005.... why not construct your own list of "Constitutional Statutes, it's a useful list to have); caselaw (similarly a list of key cases may be useful - have a think about what you would include in a 'top twenty'); and conventions.
Flexible/Rigid can also be misleading. In theory the UK Constitution is very flexible - conventions can develop and die; Parliament can change ANY rule - no need for special majorities or an extraordinary procedure. Yet it has changed less than some of the more "Rigid" constitutions that make changes very complex and difficult to achieve.
Make sure that you are familiar with the other terms - and I'm happy to answer specific questions - email me here.
Two terms to be careful with - illegal and unconstitutional - they are not the same (they might be in the right circumstances). In the UK an act may be unconstitutional (perhaps a Statute offends against one of the key features of the constitional framework - but that won't make it illegal. Where a court can strike down a law or action for conflicting with a Constitutional rule - then it can be described as illegal.