Industrial waste is processed in a different way than household garbage.
Industrial waste is processed differently than the garbage people produce in their homes.
ーIndustrial waste is processed in a different way than household garbage.
「産業廃棄物は家庭ゴミとは異なる方法で処理される」
from the one for ではなく ただ簡単に than と言えば良いですよ。
ーIndustrial waste is processed differently than the garbage people produce in their homes.
「産業廃棄物は家庭で出るゴミとは異なる方法で処理される」
in a different way の代わりに differently とも言えます。
the garbage people produce in their homes で「家庭で出るゴミ」
ご参考まで！
Industrial waste is processed differently from household garbage.
Industrial waste is processed differently from household garbage.
（産業廃棄物は家庭ごみとは異なって処理されます。）
differently from：
in a different way from（異なる方法で）の代わりに、differently（異なる方法で/異なって）を使うと、文がより簡潔になります。
カナダ 
アメリカ合衆国 
