What is the difference between "request for proposals" and "call for proposals" in the context of applying for funding?
Different funding agencies use different language for essentially the same thing---and also the same language for very different processes!

In the United States, at least, every different agency has a different process, customized to its mission and to the community that it is trying to interact with.  Moreover, even within agencies there are often radically different processes behind the same names.  For example:


With NSF, applying through the Program Solicitation for "Expeditions in Computing" is an entirely different (and much lengthier) process than for a standard NSF small/medium/large like the CCF core programs.
With DARPA, every Broad Agency Announcement has its own individual customized process, which is typically explained at the associated "proposer's day" meeting.


You really need to get to know the particular agencies that you are interested in.  A good way to do this is to meet program manager or listen to the talks that they give: program managers often attend major conferences in the fields that they fund, and in particularly organized fields, they will sometimes have a workshop at the conference in which program managers give "how to get funding from me" talks.  Another good way is to talk with colleagues who have worked with the agency before and know the ropes, or to become a partner in a collaboration with them.