fATPL doesn´t exist, it is just a de-facto term to mean that one has a CPL and completed their ATPL theory exams without meeting the experience requirements (flying hours).
In JAA land, there are 14 ATPL exams devided by subject. Also, there are 6 exams for the PPL that one usually gets before working towards the ATPL. The JAR ATPL will allow you to be PIC on European registered aircraft over 5700kg (and when I say European registered, I mean countries that are part of the JAR now EASA signatory)
In FAA land (USA), one takes a PPL theory paper, an IR theory paper, a CPL theory paper, and eventually when one is near the experience requirements for the FAA ATP, they will take the ATP paper. The exams usually only require two days of studying and they encompass all subjects in one exam of 100 questions. In the US, the oral exams, which are part of the checkrides, are pretty difficult (for example, a flight instructor checkride oral can last around 6 hours before the flight test). An FAA ATP will allow you to be PIC for aircraft for scheduled airline operations.
Training... Both routes lead to a CPL, and one usually gets a job appropriate for low time pilots until they have the flying experience required to get the ATP/ATPL.
JAA: There are typically two routes, modular and integrated. Plenty of threads on here about these two. Either route will lead you to a fATPL (remember, it is really a CPL with ATPL theory). These programs will take you about 18 to 30 months (depending integrated or modular respectively). JAA is good if you are a citizen of one of the European countries that are members of the JAA/EASA.
FAA: Two routes, part 61 and part 141. Part 141 programs have strict lesson plans and curriculum approved by the FAA and one can achieve the CPL with 190hrs. Part 61 is more of an at your own pace kind of deal, and a CPL requires 250 hrs. There are programs in the US where one can achieve 0hrs to CPL with all three instructor ratings (CFI, CFII, MEI) in literally 150 days. FAA is good if you have US Citizenship or a Green Card.
For those of us who have done both, we call the US method ¨Easy FAA¨. We also say that in USA, they teach you how to fly the airplane. In JAA land, they teach you how to build the aeroplane.
