Max M. answered 06/06/19
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All these credits are negotiated, so the truest answer is that a person or company gets a "sponsored by" credit if they negotiate for one, and a "presented by" credit if they negotiate for that.
But the answer you're looking for is that "sponsored by" pretty much always means that the person or company paid for part or all of the show. "Presented by" could mean that they actually worked on it and made creative and/or administrative decisions. Or, if that's obviously not true ("A political drama presented by McDonald's" or something like that), it might just mean that they paid for all of it, or at least a much bigger percentage of the budget than those who merely sponsored it. So if it's "presented by" XYZ *and* "sponsored by" ABC, maybe XYZ put up 75% of the budget, and ABC made up the shortfall.