When are the terms diphosphate and pyrophosphate used? On the Wikipedia article about pyrophosphate, it states that:


  The group (pyrophosphate) is also called diphosphate or dipolyphosphate.


But for example, why is ADP apparently called adenosine diphosphate but not adenosine pyrophosphate? The same for geranyl pyrophosphate (GPP) instead of geranyl diphosphate?  In which context the terms diphosphate and pyrophosphate are used?
Great question, but unfortunately without a great answer.  Chemistry is very inconsistent in its naming of phosphates.  In addition to the terms diphosphate and pyrophosphate, the term bisphosphate is also used.

Someone will probably put in an answer that cites "official" IUPAC or IUBMB rules.  In many cases (but not all) these rules are more sensical and well thought-out than the terms in common usage in the field, but unfortunately, they are not in universal (or even wide) use.

Here is a rough breakdown of my sense of how these three terms are used:

Inorganic chemistry


Pyrophosphate indicates a phosphate anhydride.
Diphosphate indicates a salt that contains more than one (ortho)-phosphate anion.
Bisphosphate is not widely used.


Biochemistry


Pyrophosphate: used inconsistently to name an organic derivative of a phosphate anhydride.  This is what you see in geranyl pyrophosphate (GPP).  It is also used to refer to "inorganic" pyrophosphate anion, often abbreviated as PPi.
Diphosphate: an unfortunate term that is ambiguous, although usage is shifting towards synonymity with pyrophosphate.  It is often used to mean "pyrophosphate" and but sometimes still used to mean "bisphosphate".  Biochemically, the most important phosphate anhydrides are undoubtedly ATP, ADP, etc.  These are never referred to as pyrophosphates even though that term would be more accurate.  History has chosen "triphosphate" and "diphosphate" as the terms to use for adenosine-substituted phosphate anhydrides, icky though the term may be.
Older literature will also use "diphosphate" to mean "bisphosphate".  The name "fructose diphosphate was formerly in wide usage for what is now known as "fructose-1,6-bisphosphate", for example.  That compound contains no phosphate anhydrides.
Geranyl diphosphate is still a fairly widely used synonym for geranyl pyrophosphate.  You see abbreviations for this molecule of both GPP and GDP.  I prefer the name GPP, but unfortunately not everyone uses it.
bisphosphate: Now in wide usage as the preferred term for an organic molecule with multiple ortho-phosphate esters, such as fructose 1,6-bisphosphate.  Biochemists have done a relatively good job of adopting this usage in modern times.  


A common confusion that stems from this nomenclature concerns the stability of organophosphate compounds. Phosphate esters, e.g. glucose-1-phosphate or glucose-6-phosphate or adenosine monophosphate, are much more stable and less reactive than phosphate anhydrides such as acetyl phosphate (a mixed anhydride of acetic acid and phosphoric acid) or the phosphoanhydride bonds in adenosine triphosphate (ATP).