Dear kwstas -
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As to the proper designation of ATPL in the USA, remember that the FAA actually issues "pilot certificates" rather than licenses (or licen
ces) as spelled in the British-English part of the world. When I started flying, the ATP was even known as "ATR" airline transport
rating rather than "ATP" - Now most of the US pilots, having been exposed to ICAO designations, now mention "FAA/ATPL" to conform to the rest of the world.
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Other practices with the US/FAA, that were different, was that until the mid-1970s, only a total time of 1,200 hrs was required to hold the ATP, rather than the 1,500 hrs now required. The US/FAA do not have a "frozen ATPL" equivalent. To take the written ATP exam, you must be 23 years old, and have a total of 1,500 hours. Until the mid-1970s as well, many if not most F/Os only had a CPL/IR, the multiengine rating was not even required. The ATP was essentially the certificate only required for captains of FAR 121 air carriers. Back then, the "regionals" were operated under FAR 135, and only required a CPL for captains. I think the passenger seat limit for the regionals was 19 passengers...
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Another notable difference with the FAA certificates is the "type ratings". To be F/O on a type aircraft (P2), the FAA does not require a "type rating" nor any is listed on the FAA pilot certificate. Only captains are required to hold a "type rating" (P1) on their certificate.
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So as you see, basically, while the finished product of "pilot training" when flying the line is essentially similar between ICAO, JAR and FAA, the licencing requirements and prerequisites are somewhat different.
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Another question you have, is regarding the well established and reputable pilot schools in USA. The ones you mentioned have good reputation. Embry-Riddle has long been established as a training facility, tied with universities education and degrees. Flight Safety International has long been known as a training facility for "corporate" type airplanes, such as Citation, Learjet or Gulfstreams, they now also compete for the "regional pilots" training market. I would like to mention two others, which have reputable "ab-initio" programs, are Sierra Academy of Aeronautics, in Oakland, Calif. and American Flyers, in Ardmore, Okla. These last two are not specializing in "regional jet" pilot training, rather, they do "ab-initio" primarily, from PPL to ATP, including CFI programs.
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Hope this lifts the "fog" on your understanding of what is "FAA training, or licencing"...
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Happy contrails