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The primary difference is that miracles come from G-d and magick comes from the absence of G-d.

Our Oral Tradition brings a conversation between Moses and Pharaoh that answers your question so I'll share it with you.

Pharoah asked Moses Who is this G-d in Whose Name he wants to release the Jews. Moses tells him and shows him a sign with casting his staff down to the ground and it turning into a snake.
Pharaoh belly laughs and tells his magicians to repeat the trick. The school children were arriving from home and he told them to repeat the trick. Everyone, from old to young, was turning sticks into snakes. Pharaoh turns to Moses and tells him he brought his wares to a saturated market. He wasn't going to make a sale there.
Moses respond to Pharaoh, Oh contrare! When you have superior wares you specifically bring them to where they are best known.

The text then says that Moses snake turned back into a stick and as a stick it then ate the snakes of the Egyptians. That element of the sign was something clearly impossible for any Egyptian to duplicate and a clear sign that something powerful was behind Moses' abilities.

Pharaoh chose denial, however, and credited Moses with being a better magician but not the truth of representing G-d.

The Torah tells us that a false prophet will do signs but if he says anything contrary to the words of the Torah, he is false.
So that's how we know. Signs are nice but they only go so far. What is the person doing the signs trying to illicit.

G-d says clearly the Torah is eternal and will not be changed and any one who tries changing it is not to be believed. They should even be taken out and killed.