Under FP7, which was the EU funding programme running from 2007 to 2013, the People Programme was offering the Marie Curie Actions. This programme considered two types of researchers:
Early-stage researchers are defined as those in the first four years (full-time equivalent) of their research careers, starting at the date of obtaining the degree which would formally entitle them to embark on a doctorate, either in the country in which the degree was obtained or in the country in which the research training is provided, irrespective of whether or not a doctorate is envisaged.
Experienced researchers must, at the time of recruitment (i) be in possession of a doctoral degree, independently of the time taken to acquire it, or (ii) have at least four years of full-time equivalent research experience, including the period of research training, after obtaining the degree which formally allowed them to embark on a doctorate in the country in which the degree/diploma was obtained or in the host country (irrespective of whether or not a doctorate was envisaged).
So you are correct to say that fellowships for experienced researchers can correspond to postdoctoral fellowships (although strictly speaking, someone without a doctoral degree might still be able to apply).
In FP7, experienced researchers could apply to four types of fellowships (together with an organisation):
- Marie Curie Intra-European Fellowships (IEF)
- Marie Curie International Incoming Fellowships (IIF)
- Marie Curie International Outgoing Fellowships (IOF)
- Marie Curie Career Integration Grants (CIG)
The calls for these fellowships are now over, and as far as I know, these terms should no longer be used (apart to designate existing fellow).
We are now under Horizon 2020, and the Excellent Science pillar offers the Marie Skłodowska-Curie actions.
An experienced researcher can now apply to an Individual Fellowship (IF), which can be either European (replacing IEF) or Global (replacing both IIF and IOF). The next deadline for this call is on the 11/09/2014, September 11 of this year.
The programme is also providing a Research and Innovation Staff Exchange call , which corresponds to the previous IRSES, but it closed on the 24/04/14 (another one should open next year). So the link you mention with Staff Exchange is a typo, and it should read Individual Fellowship (and as a matter of fact, if you click on the link, you'll reach the IF page).
If you are interested in applying for an MSCA, I'll recommend the official Guide for Applicants.