(noun) + な versus (verb) + な

Actually, I want I'm figuring out a specific sentence, which is 「暇なので相手して。」And I thought that it means "I am bored because of my companion."

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  暇 [hima] - "leisure" / "fun"

  
  


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  な [na] - Negative imperative. Meaning "himana" means "not fun"

  
  
  


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  ので [node] - "because"

  
  


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  相手 [aite] - "companion" or someone with me

  
  


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  して [shite] - "I am doing" or current state

  
  

But according to http://www.japanesefile.com/Adjectives/hima_na_1.html "hima na" means "to have free time"

Answer

暇 acts as an adjective here, which explains the な which is basically the 連体形 of the 活用語尾 (conjugative suffix). 暇 can also be a noun, but here it is not.

Your sentence means "since/because I have free time, become my partner" (lit. because it is free time, do partner).

Finally, I will answer your question assuming you meant to say: "what is the difference between (noun)+な and (adjective)+な?" (and not (verb)+な)

The basic difference between these two なs is that the な following an adjective is the 活用語尾 (conjugative suffix), whereas the な following a noun is the auxiliary 「だ」. Both conjugated in the 連体 form.

There is a very small difference between -na adjectives' conjugative suffix and the auxiliary 「だ」, which is only morphologic (meaning there is no difference in meaning): when we use an adjective in the 連体 form, what follows will always be な, for example:

綺麗な花

暇な時

好きな人

簡単な宿題

On the other hand, a noun has no conjugation, it acts on its own, and the following な (if there is) is independant because it is an auxiliary verb, and not a conjugation attached to the noun.

「厄介な」ので = adjective (because he is troublesome)

「学生」「な」ので = noun (because he is a student)

Plus, we cannot always use 「な」 (だ) after a noun, but it is okay for an adjective to be followed by な in any case.

　学生なころ X

　学生のころ O