If it helps, by "compatibilism" I mean classical compatibilism
If I take the following definition as canonical, the answer is clear:
This article [...] considers various strategies by which critics of [Frankfurt-type] examples have tried to rescue the Principle of Alternative Possibilities (PAP), or variations of it, and also considers various responses to these critics. It notes that moral responsibility does not require alternative possibilities, but also believes that freedom does imply alternative possibilities. The resulting view is called semicompatibilism.
(Abstract of Fischer, J. (2005-03-03): Frankfurt-Type Examples and Semi-Compatibilism. In Robert Kane (Ed.), The Oxford Handbook of Free Will. Oxford University Press)
In other words: (Classical) compatibilism assumes that freedom is compatible with determinism (i.e. at least in the physical world the impossibility of alternative possibilities). This is mostly, if not always, coupled with the view that moral responsibility is impossible without freedom. In other words: both freedom and moral responsibility are compatible with determinism.
Semi-compatibilism, on the other hand, holds that while freedom is, in fact, incompatible with determinism (in absence of PAP), moral responsibility is not. It argues for there being moral responsibility even in a world without freedom (of will). Hence semi- compatibilism, since it only endorses one half of what classical compatibilism argues for.