Möbliert means furnished; teilmöbliert means partly furnished and could mean almost anything. Because a Zwischenmiete is usually somebody's actual home let while they are away, it comes with their actual furniture, and the practical question is not whether there is a bed but how much of their life is still in the flat and which cupboard you may use.
Unfurnished, in the German sense, is more unfurnished than most arrivals expect. A long-let unmöbliert flat routinely has no kitchen at all — no cabinets, no worktop, no appliances, sometimes not even a light fitting, just cables from the ceiling. Tenants buy and install a kitchen and take it with them, which is the origin of the whole Ablöse business.
Furnishing also has an effect on price and regulation that is worth knowing. Berlin's rent controls bite on ordinary long lets; furnished, temporary and short lets sit outside much of that, which is precisely why so much of the city's stock has migrated into furnished short-term letting. You are paying a premium for flexibility, and it is a real premium, not an illusion.
Two things to establish before you commit: whether there is bedding and kitchen equipment, which is easy to assume and expensive to discover at 11pm on moving day, and how much storage is actually free. “Fully furnished” and “two empty drawers” coexist more often than anyone admits in an ad.