Any word read in on'yomi in Japanese and using the Sinic hanja reading in Korean is probably ultimately attributable to Middle Chinese, unless evidence can be found of an independent coinage somewhere on the Japanese archipelago or the Korean peninsula.
Terms like the ones below are likely borrowings from Middle or later Korean, rather than Chinese. We can guess at this even before delving into the etymologies simply because the readings do not fully conform with the regular kinds of on'yomi for Japanese kanji. For instance, 温突 in normal on'yomi would instead be ontotsu, 妓生 would be gisei, and 明太 would be meitai or myōtai.
- 温突 [おんどる] /(n) (uk) Korean floor heater (kor: ondol)/
- 妓生 [きいさん] /(n) Korean female entertainer (kor: gi-saeng)/
- 参鶏湯 [サムゲタン] /(n) samgyetang (kor: samgyetang)/chicken ginseng soup (Korean dish)/
- 総角 [チョンガー] /(n) (uk) bachelor (kor: ch'onggak)/
- 沈菜 [キムチ] /(n) (uk) kimchi (kor: kimch'i)/kimchee/spicy Korean pickled cabbage/
- 明太 [めんたい] /(n) walleye pollack (Theragra chalcogramma) (kor: myeongtae)/Alaska pollack/
Some words in kanji have multiple readings, where one is from Middle Chinese and one from Korean. 両班 can be read as yanban, indicating an aristocrat in middle-ages Korea, or it can be read as ryōban, indicating both the east and west lines of statuary in a Zen temple.
Looking into sound correspondences discoverable from kanji / hanja readings, other patterns begin to emerge. For instance, Japanese 蜂 hachi ("bee") is probably cognate with Korean 벌 beol. Old Japanese initial /p/ developed into /w/ and /h/ in modern Japanese, while kanji ending in /chi/ in the on'yomi pretty consistently match hanja ending in /l/ in the Korean. The slight mismatch in the vowel is an uncertainty; we do know that OJP vowels had different qualities from the modern ones, and this might account for the shift.
* JA /hachi/ → OJP /pachi/ → KO /pɘːl/
However, this is very likely a case of cognates: words sharing a common root that have been in the respective languages since some theorized point of divergence, rather than borrowings that moved from one language into another.
About 幸 sachi and 살 sal, the sachi reading also refers to a hunting tool, possibly a kind of arrow. This reading again fits with the sound correspondence patterns, suggesting another cognate:
* OJP /sachi/ → MK /sal/
About 熊 kuma and 곰 gom, see Talk:구름 and 黒#Etymology_2. The upshot of this is that there is a cluster of likely cognates surrounding the JA and KO terms for "cloud", "black", "hole", "bear", and "spider".
About 鶴 tsuru and 두루미 turumi, these are probably also cognates. See the etymology sections at 鶴#Japanese and 두루미#Korean -- there are cognates in multiple regional languages, including Mongolian and Turkish.
About 塚 tsuka, my JA materials state that this is cognate with OJP verb 築く tsuku ("to build up earth or stone into a structure"). The -a ending on the noun tsuka would suggest the mizenkei or incomplete form of the verb tsuku, suggesting an original meaning of "that which is being built up into an earthworks (but isn't finished yet)". That said, the incomplete is also the root of the passive form of all verbs, so the original meaning might simply have been the passive sense of "that which is built up into an earthworks".
Given also the wide range of meanings and deep prevalence of the OJP verb tsuku throughout the history of the language, and the close semantic overlap between the various senses of tsuku, I would be very surprised indeed if tsuka were a loanword. I would be much more open to the possibility that it is cognate with a Korean term.
Other cognates not yet listed above probably include:
- OJP 沼 nu and KO 늪 neup "swamp, marsh"
- JA 島 shima and KO 섬 seom "island"
- JA 日 hi and KO 해 hae "sun"
- JA 星 hoshi and KO 별 byeol "star"
- OJP 火 pu and KO 불 bul "fire"
- OJP 水 mi, mizu and MK 밀 mil, KO 물 mul "water"
- JA 事 koto and KO 것 keot "thing"
- OJP 海 wata and KO 바다 bada "sea, ocean"
Other borrowings not yet listed above include:
- JA チャリンコ charinko "bike", apparently from Jeju dialect 자륜거 jaryun-geo.
- JA 大后 konioruku "emperor's wife", stated in JA dictionaries as coming from old Korean kon or koni meaning "great" (possibly 건 geon "rich"?), with the oruku part meaning "wife", but I have no idea what the KO term would be.
- JA 王 kokishi, konikishi is also from some variety of old Korean, with the same koni element, and kishi apparently meaning "king, lord, ruler".
- JA 夫人 hashikashi "husband", apparently borrowed from a Baekje dialect word.
- JA 百済 Kudara "Baekje" is probably also from a Baekje dialect word (the Chinese-derived on'yomi of Hyakusai is another JA term for "Baekje").
Sorry that's so long, but I hope it's useful. Feel free to ping me on the EN WT. At a bare minimum, I might know where to look things up. :)