Difference between Present Perfect and Present Perfect Continuous [duplicate]

I know this question has been asked a lot, but I still don't fully understand the difference between Present Perfect and Present Perfect Continuous (if there is one).

Sometimes the two tenses are interchangeable[...]. But sometimes they are not. Essentially, it depends on whether the action denoted by the verb is regarded by the speaker as completable or not. By this definition, living and learning, for example, are not completable, in which case both tenses are possible:

-I have been living in London since 2001.
-I have lived in London since 2001.

Is one of these tense carrying more sense regarding the fact that I am/am not currently living in London?

It has been 13 years I am living in London

Is it grammatically correct? If yes, would it be closer to Present Perfect or Present Perfect Continuous? Does this mean that I am still living in London?

No, I can't find a difference in meaning between the first two sentences.

Your third sentence is not idiomatic English: you've gone for the present continuous, which is only used for the present or future, and never for a time span in the past even if it extends to the present.

It has been thirteen years that I have lived in London.

is just possible, but feels very awkward. This is clearly intended as a fronted version of

I have lived in London for thirteen years.

presumably to emphasise the time; but the only natural way I can think of to say this is

Thirteen years is how long I have lived in London.

More natural is a different construction:

It is thirteen years since I came to live in London.

but this doesn't necessarily imply that I have lived here all that time.

More colloquially, you might hear

Thirteen years I've been living in London.