Well, specifically, it implies an open source license under the OSI definition, which happens to be almost identical in a licenses covered to the Free Software definition from the FSF.
It might to you, but it shouldn't. The definition of open source is not controlled by the OSI; they only organize licenses and certify licenses as OSI-approved. However, you don't need an OSI-approved license to be open source. There are many open source packages that are not under an OSI license--most famously, SQLite.
You don't need to use an OSI-approved license to be Open Source, but you need to use a license that complies with OSI's Open Source definition. Otherwise, the term would be meaningless.
They didn't invent the term. The term was invented first. The OSI was founded later. See the OSI's own post on this [1].
A much more detailed discussion of the origin of the term and its initial use appears here [2]. The latter link in particular is interesting reading, because it includes the political dimensions (especiall w.r.t O'Reilly's difficulties with the FSF).