Its my pleasure to be of any help with your queries. And trust me I understand your confusions. Just a few months back my MIL had similar questions regarding the slaughter and believe me answering you guys here virtually is far easier than answering my family and In laws!
And yes Adey is correct here. Its actually the lack of a better word to use that we call it "qurbani" or "sacrifice". The Arabic word "hady" makes more sense I suppose.