The difference is whether it is supposed based on certain evidence(=はず) or it is supposed one's subjective assumption against things without any evidence. (=ちがいない) 家に明かり(light)がついているから、誰かいるはずだ。 雰囲気(ふんいき)からみるに、あの人は警察官にちがいない。 ‥雰囲気(ふんいき one's "atmosphere" including the appearance) Seen from the atmosphere, that person must be a police officer. It's like the difference between "No way!" and "It can't be!" I guess, when it comes to a denying expression. はず is written "筈" in Kanji, which means a notch(nock) of an arrow. Without the notch, "there's no way" that you can hit the target with the arrow, that's the origin of はず that it's said, it's interesting haha So you can almost think はず as "the reason" for a sense. ちがいない is like "I'm sure" in English. You're sure without any certain reason based on any proof, but you strongly think so anyway.