There's no fixed scale, and therefore the miniatures are all over the place, from woodchip and nano (played with tweezers) to travel models that are just a notch off a soprano scale length. Kala makes some as well, besides Ortega, iUke and some independent luthiers.
Which brings me to the names. I believe Ohana patented the sopranino and sopranissimo indications, a bit like Hohner forced its competitors to call their melodicas something other than 'melodica': melodeon, melodion, pianica. There are three very distinct families of musical instruments called melodeons (foot-pumped organs, diatonic bisonoric accordeons and mouth-blown keyboards)! Shop often use 'sopranino' as an umbrella term for smaller than usual ukuleles, but the brands themselves go for lots of different terms.