Not to say sometimes there's a huge difference between hanzi and kanji that makes very little sense: my favourite example is 泥棒 (Chinese ni2 bang4, Japanese dorobou). The meaning in each language is quite startling: "mud stick" versus "thief" (!).
Don't forget:
English: greengrocer
Chinese: 菜贩 (literally "vegetable vendor")
Japanese: 八百屋 (literally "house of eight hundred")
Seriously, what the heck, Japan?
Actually in Japanese, 食べる (taberu) is just one type of word for of "eat". 食う (kuu) is another, (more informal/common?) word for eat, and I believe it can also be applied to "eating" abstract things like consuming time or defeating an enemy. I have no idea if it's used to informally mean "capture" in some context too, but I wouldn't be surprised if it is.
But you're right, it differs from the modern Chinese 吃. Of course, since it drew its roots from an older form of Chinese it's not totally unrelated; 食用 in Chinese also means "to eat" for instance. Japanese kanji usually have Chinese origin, but sometimes Chinese characters have no Japanese equivalent kanji.
To me, Chinese was a great help when learning Japanese (I learnt in that order) since the kanji were all fairly readable. In fact it's the only thing gluing my terrible Japanese together, since it's like an instant boost of several hundred vocab items.
Not to say sometimes there's a huge difference between hanzi and kanji that makes very little sense: my favourite example is 泥棒 (Chinese ni2 bang4, Japanese dorobou). The meaning in each language is quite startling: "mud stick" versus "thief" (!).