Here's how I see it.
The term "shaman" that we now usually use as a generic term (for someone who serves their community by going into trance and then talking to spirits) originally comes from a Tungusic language of Siberia. Other shamanic cultures have their own terms for that role (and often intensely dislike being subsumed under the "shaman" term), and their own traditions associated with it. Many people believe that there were shamanic practices in most cultures at some point in history, if you only go back far enough.
Then American anthropologist Michael Harner came along in the early 1980s and created what he called "core shamanism," that is, a set of shamanic techniques that (according to Harner) were detached from any specific culture and common to most of them. This kind of shamanism is basically what is taught in most Western workshops that teach these techniques to groups of people. The Foundation for Shamanic Studies teaches these workshops the way Harner initially developed them, but there have been countless others who have at least been influenced by the idea of core shamanism, whether they directly credit Harner or not.
Some people have then started to reconstruct or reinvent shamanic traditions that haven't survived in an unbroken line (like they did in several indigenous cultures), e.g. Celtic or Northern Tradition shamanism. This is more or less based on the surviving anthropological evidence and lore, and some people also claim they have been spirit-taught about certain aspects of a tradition. That means, they are going back to a culture-specific cosmology, like it also exists in indigenous shamanisms elsewhere. Some of them do this in order to avoid appropriating other cultures' traditions and instead look to their own ancestors' traditions (which then brings up the whole messy question of ancestry and all the issues related to that).
And then there are of course many people who have invented/developed their own shamanic cosmologies, often by taking bits and pieces from existing traditions and mashing them together. After all, there is money to be earned with shamanism in the West, and therefore people try and create their own "brands" of shamanism (sometimes complete with trademarked names) to differentiate themselves from each other. Personally, I am highly suspicious of these attempts and cringe whenever I see someone vaguely refer to "the" Native Americans, or claim a teaching lineage that they are unable to prove, or one that is considered downright fraudulent by the people who actually belong to a particular indigenous nation/tribe.
Personally, I have started out learning shamanic techniques like they are taught as "core shamanism" but eventually found that it didn't feel right to me to do this stuff outside of a greater cosmology/spiritual tradition. Right now, my shamanic practice is mostly on hold while I try to clarify my position in relation to the existing culture-specific traditions.
I'm not sure if this answers your question, but it is what I wanted to say about the different kinds of shamanism that apparently are around. For basic information about shamanism as it is practiced around the world, I highly recommend the Wikipedia article on the subject:
http://en.wikipedia.org/wiki/Shamanism.
