There seems to be many regulation bodies across the globe, how are they different and how are they alike? Specifically, how is ICAO different from the rest?
ICAO is the International Civil Aviation Organization, a specialized agency of United Nations. It was created after the Convention on International Civil Aviation (the Chicago Convention) of 1944 was ratified in 1947. The purpose of ICAO is according to the convention:
"WHEREAS the future development of international civil aviation can greatly help to create and preserve friendship and understanding among the nations and peoples of the world, yet its abuse can become a threat to the general security; and
WHEREAS it is desirable to avoid friction and to promote that co-operation between nations and peoples upon which the peace of the world depends;
THEREFORE, the undersigned governments having agreed on certain principles and arrangements in order that international civil aviation may be developed in a safe and orderly manner and that international air transport services may be established on the basis of equality of opportunity and operated soundly and economically;
Have accordingly concluded this Convention to that end."
Within ICAO, the 191 Member States and a number of global aviation organizations work together to develop international Standards and Recommended Practices (SARPs). These SARPs are the reference for states developing their national civil aviation regulations which are legally enforcible. This is an important aspect: ICAO SARPs are not legally binding by themselves, they form the basis of national regulations which have legal status.
In this way civil aviation regulations are harmonized all over the world, with slight differences based on the actual implementation in national regulations. These local differences are then reported back to ICAO and published.
CAA is the Civil Aviation Authority. This is a generic term used in many countries, notably the UK and China. A CAA is a national regulatory body responsible for aviation. The CAA implements the ICAO SARPs in national legislation and is responsible for regulatory oversight.
FAA is the Federal Aviation Administration. As the Civil Aviation Authority of the USA, it is responsible for establishing aviation regulations in the US. These are known as FARs (Federal Aviation Regulations).
In addition to its regulatory role, the FAA is also responsible for Airspace and Air Traffic Management, maintenance of Air Navigation Facilities infrastructure and has an active role in Research and Development of aviation related systems and technologies.
JAA were the Joint Aviation Authorities, a co-operation of most European (EU and non-EU) civil aviation regulatory authorities. It was not a regulatory body itself, the member authorities were responsible for the regulation.
Originally started as the Joint Airworthiness Authorities in 1970 its objectives were to produce common certification standards for large aircraft and aircraft engines to facilitate a European aviation manufacturing industry (Airbus). Over time, the scope was extended to included aircraft operations, maintenance, licensing and certification/design standards for all classes of aircraft.
With the creation of EASA (see below) in 2002, the EU members transferred the airworthiness regulations away from the JAA. Over time, EASA became responsible for operations and licensing as well. In 2009 the JAA system was disbanded. Only the training organisation (JAA-TO) remains, it mainly provides courses for CAA staff of European countries.
EASA is European Aviation Safety Agency. Created in 2002 by the European Commission, EASA took over the functions of the Joint Aviation Authorities of the EU countries.
The responsibilities of EASA include drafting of aviation safety legislation and providing technical advice to the European Commission and to the EU Member States, airworthiness and type certification of aircraft and aircraft parts for aircraft operating in the EU, approval of aircraft design organisations world-wide and of production and maintenance organisations inside and outside of the EU.
Since its creation, the competences of EASA have gradually expanded. This process is still going on.
Let me give you a brief description of all the authorities you mentioned (as far as I know them). I hope this will help you and answers your question.
ICAO - The International Civil Aviation Organization is was founded to set up international standards in aviation. When international air travel became more and more present (1947) there was a need have international regulations. The ICAO counts 191 member states and all have to adopt their guidelines or advice the ICAO of regional differences, which will then published by the ICAO.
FAA The Federal Aviation Administration is the aviation authority of the United States of America. It is responsible for setting up the federal aviation regulations (FAR), which are binding for all flight operations in the US. The FAA also provides air traffic control service at most control towers and all en-route air traffic control centers.
EASA - The European Aviation Safety Agency, former Joint Aviation Authority (JAA), is best described by taking both names: It's the European aviation authority. I personally (on my license it still says JAA) don't see the advantages of EASA compared to JAA. I've heard that they are aiming for a 'Single European Sky', which I would really appreciate, but it also costs a lot of money and means a bunch of new paperwork. Let's return to your question as an authority you can compare EASA to the FAA, but you need to remember that it is still an international and organization, so even if they are small, there are regional differences.
CAA - Honestly I don't even know what the abbreviation stands for, but as far as I know it's the Chinese aviation authority and a governmental organization of the republic of China. It's also Civil Aviation Authority for UK.
As you see, all of them are there to establish rules for aviation in order to make it as safe and efficient as possible. The ICAO is international and responsible for very basic - they are still complex - general rules. The other authority are making there regulations according to, or at least, based on the ICAO standards.
ICAO was explained.
CAA is rather common name for aviation authorities in the country. Like police for law enforcement. But different countries call the same differently. Like in Russia they have name milicija for police Here is a complete list of CAAs: https://en.wikipedia.org/wiki/List_of_civil_aviation_authorities
FAA is mega scale CAA for americans. EASA is mega scale CAA for European union.
Small countries usually follow FAA or EASA or other big authority.