に相違ない・に違いない: the difference
に相違ないN2
Meaning
Without a doubt, Certainly, Surely, Not mistaken
Past papers
Example
この下駄は彼の物に相違ない。
There is no doubt that these geta are his.
に違いないN3
Meaning
There is no doubt that, I'm sure
Past papers
Tested 4 times in past papers
Example
あの顔立ちからして、日本人に違いない。
Judging from that face, he must be Japanese.
How to tell them apart
「に違いない」: same meaning, fine in writing and speech.
「に相違ない」: more formal, like an official document.
「はずだ」: 'should be so' by common sense, and you would be surprised if it were not; 「に相違ない」 means the speaker is certain.