the 2 sentences are the same in meaning but... "I got to go now" is not correct in grammar because 'got' is not a helping verb that links the subject and the predicate correctly. It is best to just say "I have to go now" because it is grammatically correct since 'have' is a linking verb.

The two phrases are exactly the same in meaning, but "I have to go now" is the more formal and in everyday conversations, especially in internet language, "I got to go now" and "I gotta go now" are more commonly used.