"Give them more apples."
Translation:उन्हें और सेब दो।
So these are two different meanings of the word "more" in English. ज़्यादा can mean more in the sense of "a lot" or even "too much", or "more than something else" (as in इस से ज़्यादा, more than this). It's for comparing amounts, traits, frequency, etc.
और is used for "more" of stuff: you had some, and you'd like an additional amount of it. Think of this as a useful word to use when dining: मुझे और चाय दो दीजिये is something like "Could you kindly give me more tea?" Another beer, more rice, etc.