Uhm..right..I've been putting off answering this question for quite a while now...simply because I'm not 100% sure of the correct answer. But to put it simply - yes, when you say "daj mi chleba" it kind of indicates that you want a slice/few slices of bread, whereas if you say "daj mi ten chlieb!" it sounds as if you wanted the whole bread... HOWEVER, I don't think the use of this variation is as strict as in Polish. If you say "daj mi chlieb" instead of "daj mi chleba" I can guarantee you won't have any problems being understood. People kind of use the two interchangeably anyway.
If you ask a random Slovak person "What's the difference between 'daj mi chlieb' a 'daj mi chleba' chances are they won't be able to tell you the difference.
Hope that helps a little.
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