On the other hand, I think I may also be failing to explain this correctly because we are already at the limits of my English :)
If you can just write one example in Turkish, of each case, so three total, most readers can probably puzzle it out with enough time using translation tools.
> Polis, toplumun güvenliğini sağlamakla görevlidir.
> (Police are responsible for maintaining public safety.)
Police Force as an Organizational Unit:
> Bu şehirdeki polis teşkilatı faaliyetlerini arttırdı.
> (The police force in this city has expanded its operations.)
Specific Police Force Within a Specific City:
> İstanbul polisi son zamanlarda çok aktif.
> (The Istanbul police have been very active lately.)
Interestingly the -ki suffix here was borrowed from Persian (another Indo-European language like English), and effectively highlights a unique instance - "the one which" - in a way that Turkish otherwise doesn't specifically do.
Sources: Me being a native speaker and also: Turkish Grammar (Oxford 2nd ed. 2001), Geoffrey Lewis. Pages 69 and 211 (Just checked to be sure).