I'm a huge fan of Jazz III's, and I've managed to get them in 4 kinds of plastic. I will give my opinion of these:
Red - Nylon
The classic Red Jazz III is the warmest sounding of the lot, and has the most friction against the strings. These are my favourite as I feel more in control, and prefer the tone. Some people complain about the grip - I've never had issues.
Black - Stiffo
Curiously named "stiffo", they have a brighter sound than the Reds, and feel smoother against the strings. Slightly better grip. Not majorly different overall.
Translucent Yellow - Ultex
The brighest sounding, and these slice through the strings! Shred-heaven with these, if that's your thing. Plenty of attack; the dynamics of your picking are very clear. I don't wear picks out very much, but these are basically indestructible. They don't wear. I loved these when cramming as many notes into a beat was the standard thing to do, but nowadays when I prefer control, I feel these go through the strings a little too well for me. These tend to get a bit slippery during playing, too.
Purple with everyone's favourite tortoise - Tortex
Also a bright sounding pick, and of course a bit different to the usual tortexs given the Jazz III shape, but it's got the same character. Much better grip than all the ones before.
Overall to answer question 1
In my experience, alongside these picks having identical shape/size, the type of plastic used has considerable consequences. I've always been curious about Red Bear picks. These are inexplicably expensive picks which come with a warning to not let them get wet, but they claim to be something to the effect of 'the next best thing to tortoise shell' and it's all apparently down to their unique material. I've never had the luck to try a tortoise shell pick, but given how prized they were, Red Bear picks are certainly enticing.