In general, the Present Perfect Simple (PPS) is used to talk about an event which happened in the past but which has a very strong connection to the present:
I have just finished laying the table so we can eat soon.
The Present Perfect Continuous (PPC) on the other hand is used to talk about an event which started in the past and it still going on now:
I have been cooking since early this morning but I will finish soon.
Having said that, however, the two tenses overlap a lot and which one we use is often an arbitrary decision and both are equally acceptable:
I have lived here since 1978.
I have been living here since 1978.
Some people believe that by using the PPC we are putting more emphasis on the action:
I have been living here since 1978; yes, in this very house; living here every single day of my life!
Contrast this with the PPS in which the time element is more important:
I have lived here since 1978; imagine that, 1978. over 30 years ago!
And sometimes the PPS is more focused on the result of the action:
I have lived here since 1978 and I think that it’s time I moved; this place is horrible!
Because the PPS is more about the result, we tend to use it when the action is completed:
I have lived here since 1978 but now I’ve bought a new house and I’m moving there today!
Again, contrast this with the PPC where the action could well be continuing now:
I have been living here since 1978 and I intend to live here for the rest of my life!
Present Perfect Simple in English Grammar – about the PPS
Present Perfect Continuous in English Grammar – about the PPC
Simple or Continuous Verb Form? – in general, which to use