Starting with very basic definition of written and unwritten constitution A written constitution is a constitution which has all its provisions codified in a single document whereas an unwritten constitution is a constitution whose provisions are not in a single document or can simply be referred as uncodified. But just this definition can't define these two kinds of constitution wholly since there are many laws which are not written but are part of a written constitution. Similarly an unwritten constitution doesn't imply it is not written anywhere- it is written but not in a single document, and on comparing constitutional document of various countries we can find that many countries with unwritten constitution actually have more documents than those having written constitution.
Differences between Written and Unwritten constitution
What makes Indian constitution a written and British constitution unwritten Inspite of Indian Constitution having many similar points with British constitution and we adopted lot of things from their constitution, the Indian constitution is still called "written" whereas British constitution is "unwritten". Also these two constitutions have most of the differences mentioned in the above paragraph but one major difference among them is-
How Indian constitution came into existence? Indian constitution was formulated by the Constituent Assembly which met on 13 Dec 1946 for the first time, in which specific persons were assigned specific tasks to deal with and then each and every point of constitution was discussed and analysed in detail before adopting it as a law, this analysing was done by various committees and after approval from all drafted by the drafting committee which was headed by B.R Ambedkar. It took to 2 years 11 months and 18 days in the whole procedure of formation of Indian constitution. And a copy of this constitution was given to all the members of constituent assembly.
How British constitution came into existence? British Constitution evolved with time and its journey started when Bill of Rights (1689), which established the supremacy of Parliament over the Crown caused the forcible replacement of King James II (1685–88) by William III (1689–1702) and Mary (1689–94) in the Glorious Revolution (1688). After this, parliament become supreme, formulating laws and this process is still going till today thus their is no specific time in which British constitution came into existence as it is still evolving, and there is no specific book of British constitution.
Countries with written and unwritten constitution The difference why some countries have written constitution while others unwritten constitution can be understood by the history of those countries, and how these countries came into existence. It's not the case with all the countries but with most of them, the seed of the way they adopted constitution lies in their history. For e.g.- countries like India, U.S.A, Srilanka etc, which were once colony of any other empire and got freedom at a certain moment of time, adopted a written constitution by making a codified single document for all the laws; whereas countries like United Kingdom, New Zealand etc, which were once monarchy, and thus evolved their parliamentary system with time and coordination with monarchy, made their constitution to be evolved in the same manner which is visible in the number of documents they have and thus it became an unwritten constitution.