Okay, from my AE perspective, and to review from the Marmelade/Konfitüre thread:
jelly - clear, no bits of fruit
jam - thicker, contains mashed fruit
preserves - very thick, with larger intact pieces of fruit
marmalade - citrus preserves, usually with some peel, mainly orange
puree - blenderized fresh, somewhat liquid, few other ingredients added, not strongly sweetened, no gelatin or thickener; made fresh, not stored in a jar (except baby food); not the word for anything spread on toast at breakfast
applesauce (one word) - lightly pureed apples, coarse texture, not heavily sweetened, eaten alone or with potato pancakes; not usually spread on toast
apple butter - dark, sweet, smooth texture, thicker than jelly, smoother than jam or preserves, spread on toast
The problem is that different fruits can use different words: grape, apple, mint jelly; strawberry, guava, blackcurrant jelly or jam; fig, strawberry preserves; orange marmalade. 'Jam' seems most common in BE; we use it too in AE (maybe more in the north?), but probably more often say jelly (thinner) or preserves (thicker).
Plums aren't as common on this side of the pond, but I've heard of both plum jelly (clear & pale, probably more typical in the US) and plum jam (in books from the UK). I agree that 'plum jam' is not hyphenated (nor are any of the rest of these).
Plum puree would sound to me like something exotic a chef made in a restaurant by putting fresh plums in a blender, not something you would buy at the store or make at home. (It does actually make me think of moo shu pork, but that's plum sauce. (-; )
Based solely on the description I could also envision, theoretically, calling this Pflaumenmus stuff plum butter, even though I've never heard of any 'butter' in this sense other than apple.
I've never heard of 'cheese' in that sense, but guava anything sounds good ...