I am not sure the decomposition between "traditional" and "jihadi" is the best one. I would rather say quietist, political activists (rather recent if you exclude holy war partisans), and holy war partisans.
Salafism is quite well summed up in the wikipedia page :
The Salafi movement or Salafist movement or Salafism is an ultra-conservative reform branch or movement within Sunni Islam that developed in Arabia in the first half of the 18th century against a background of European colonialism. It advocated a return to the traditions of the "devout ancestors" (the salaf).
So far, it means you dress, pray, eat, live, ... according to the sacred sunni texts (quran & sunni hadith), with the salafs as role models.
However, these salafs wanted to establish an islamic state, and even fought wars for it. What to do about it ? What to do about the current government, assuming you already have freedom of religion * ?
First option: don't care. This is what salafi quietism means. This movements considers that mere mortals would be unable to establish an islamic state, so they shouldn't try to do it. It can also mean to wait for the mahdi, the person in charge of establishing an islamic state before the final judgement (who may be a "reincarnation" of the prophet, I am not sure about that, I confess that religion uses words without enough clarity behind them for me).
Second option: care. It can mean to engage in politics, like what some salafists did after the egyptian relovution. They got engaged in politics separately from the already in place islamist parties. In Tunisia, some founded the party Jahbat al islah. Or, it can also mean wage a holy war, what is usually called "jihadi salafism".
Note that there is an ambiguity with the term "jihad", since some people are calling to reform its meaning. There is none with the term "holy war" or with the activities of the list of groups mentioned in the wikipedia article for "salafi jihadi".
As for "who are they" like in a list of names and their locations, I think a lot of governments would like to know this...
*This can be problematic to define depending on what the religion is asking for.