In this context (i.e. when making suggestions etc.) there is no real difference in what they mean. The basic difference is that "sollen" is "should" or "supposed to", while "wollen" means "to want/wish", it expresses aspiration or intention. The difference becomes more obvious when you use them in a different context:
Du wolltest doch mit dem Rauchen aufhören (I thought you decided to quit smoking)
Du solltest doch mit dem Rauchen aufhören. (You were supposed to quit smoking (weren't you)?
In this case, "sollen" implies that there is a specific reason besides the persons intent, like a recommendation from a doctor, a develloping disease etc.), while "wollen" simply means that the speaker thought the concerned person had the intention to stop.
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Has difficulty understanding even short answers in this language.
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