Generally the PS1 uses a fairly standard iso 9660 file system (as in pop it in your computer's CD drive and you can read the files quite happily), not sure offhand what particular restrictions and limitations. PS2 uses the equivalent boring and basic DVD one, though again I am not sure what restrictions it might impose (there are various levels that do different things but let's skip that for now).
The trouble comes in that unlike later systems then there were few standards at the time, and unofficially all the various CD ripping and burning programs competed against each other (nero with NRG, clonecd with its one, cdrwin and a few others being more popular but plenty of others). This tends to mean today you can burn whatever you like (good old imgburn probably handling most things out there) but pulling apart and reassembling can be tricky. Many then get the original game and rip it themselves to spare hassle, at least until it comes time to patch the thing and someone wants to use their vintage iso.
Bin could be a few things. The general one most people note is bin+cue (possibly plus a bunch of audio files*) wherein there will also be a cue file to tell it what goes where.
*the PS1 was among the first to have the mighty powers of CD audio rather than chiptunes from before. This means many audio tracks are just CD tracks (try putting PS1 games in CD players, skipping the first track and going from there) and rather than have 40 something meg wave files for each audio track modern emulators and file sharers might convert to MP3 or something to have others convert back later if necessary (many emulators and possibly some of the drive emulators supporting such things).
There are a handful of freeware programs that might attempt to unpack and rebuild at least basic ISO but most then find themselves instead playing with various commercial efforts. Ultraiso, magiciso, IsoBuster, possibly some of the paid versions of Daemon Tools... you can poke around on https://en.wikipedia.org/wiki/Comparison_of_disc_image_software
to see options.
Additionally then various companies did go outside the standard iso 9660 stuff, more on the PS2 though. Audio for Square/Square Enix games being one of the more notable of them. It is referred to by a few different names but raw LBA (LBA = logical block address, a way of sacrificing a bit of space to make addressing a bit easier on larger file systems) is probably the most noted version. The idea being the basic iso 9660 or DVD equivalent has its files and a boring ripper might grab those, the console however in normal conditions won't care and will happily toddle off to grab files wherever it is directed by the game's code but lo and behold the boring and basic ripper did not know about such things and missed them. Also means ROM hacking tools only looking at that will not see them either and you get to find them manually.
I will also note Spyro has a fairly interesting anti piracy protection you might also find yourself running up againsthttps://www.youtube.com/watch?v=4GYSeXLr5sY