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I think these two names have the same meaning, being from the Old Germanic personal name Warinhari, which is made up of words meaning "protection" and "army". Forms of this patronymic occur in other Western European societies, e.g., German Werner and English Warner and Garner, though these last two can have other origins. So a common meaning does not equal a common origin.
However, it may be that a French influence is at work on the mainly Piemontese Garnero, as the more widespread Italian forms of this patronymic begin with GUA, like Guarneri, Guarnieri. There is also a surname Guarnero, which, like Garnero, is mainly Piemontese, though less common.