In the first example, there's almost no difference at all.
In the second, "the hospital" would be a definite hospital -- we use "the" to mean, "you know which hospital I am talking about". If you tell me that Jim is in the hospital, you assume that I know where to find him without having to ask any further questions. But if you simply say he is in hospital, it could be any hospital: the point is he is receiving hospital treatment.
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