The double genitive isn’t something I’ve taught much, but in simple terms I believe it’s where a possessive follows the pronoun of, to create a reversed possessive.
“Jane’s friend” (regular possessive) -> “a friend of Jane’s”
Its purpose is rather flexible, it can just be used as a matter of style to create variety in the way we describe possession, but I’d say it also adds emphasis on the first noun, rather than what the noun belongs to (in the example above, meaning we emphasise “friend” instead of belonging to Jane).

Hi Sana,

Yes, if you mean the difference between the present perfect and present perfect continuous, then you’re right the two meanings can be very similar and sometimes they might overlap. Generally, there are a few distinctions, though these are not firm rules: the progressive is used more for shorter-term actions, so more recent ongoing activities, while the present perfect could be for longer-term processes; the perfect progressive would be used more for ongoing processes, that continue uninterrupted, while the present perfect is more likely to discuss ongoing actions that repeat or recur, perhaps only occasionally; and finally the present perfect tends to emphasise how long something has been done for, while the perfect continuous emphasises the process. I hope this helps.

Phil