I am by no means an expert on these, but I will try to convey what I have been informed of from people throughout the world about these different Adeniums.
First Adenium is the Genus name. Aware I am sure. Without getting into the taxonomy of the Genus.
Arabicum is one of the species of Adenium. Thai Soco's as we call them are infact a mutation of sorts of an Arabicum. Some could say hybrid, cross that the Thai people have done over the years.
Thai Socotranum and True Socotranum (from Island of Socotra) are NOT the same tree and not to be confused.
The " Thai Socotranum" is only a Thai Socotranum if it holds the traits in which they are to have to be given the title. A bit taller in the trunk (caudex) branches to be growing in a naturally forming horizontal plain and leaves to be smooth without hairs. So if you purchase Thai Soco seeds, as with any Adenium (i.e.blooms not true to 'obesum' parent from seed) they do not produce necessarily true to pod or pollen parents.
There are so many crosses being produced now with Thai Soco's, Arabicums, obesums, etc., that they are becoming so inter mixed that it is difficult to know or to put an exact name to one.
As Kadie has made a very comprehensive list above. Wonderful by the way.
The Arabicum is known as Arabicum and the Thai Soco as a TS.
If you where purchasing a tree, then looking for the characteristics required to call it a TS is what you would want to do. If buying seeds, then it would be a percentage that could possibly give the results, but you would not know until the seedlings where a few years of age.
I am going to see if I can load this information I have, but I want to ask first before doing so.
Rick
A year later, after nearly killing a "desert rose" cutting that someone gave 15 years prior, I found out about adeniums through research to save it. My adenium, "Bilibong," is approximately 32 years old now.
