In English it isn´t possible to say "nothing", "noone", "nowhere"... in negative sentences. Those words are only used in affirmative sentences because in English we can´t "negate" twice. For example, "I know nothing", "there´s noone at home"... and if you say "I don´t know nothing" it´s grammatically incorrect. That´s why, in negative sentences we use "any-": "I don´t know anything", "there isn´t anyone at home"...
However, in Spanish it´s possible. We can say "No sé nada" or "Nada sé" and both are correct. You only have to be carefully with the word order because if it´s before the verb, the sentence has to be affirmative - nada sé / nadie come/ ... - but if it´s after the verb, the sentence has to be negative - no sé nada / no come nadie ... And there´s no difference between "nada sé" or "no sé nada", they´re synonyms.