ITIL talks about three types of Service providers:
a) Internal Service provider – This represents IT departments/service providers embedded within business units in organizations.
b) Shared service unit – which provides services to multiple business units within a corporate and
c) External service provider – which represents IT departments/Service providers external to the business organization.

Now, there is no ambiguity regarding these definitions.  But I used to get a bit doubtful when somebody asks a clarification on the same such as:

Look at a scenario of a service provider who provide services to internal as well as external customers. How do we fit them into this classification:
a) As a shared service unit? – I used to agree with this initially; but was not really convinced fully.
b) As a combination of internal and external? or shared and external? – May be. But that also didnt look convincing to me.

Then, reading the section in the ITIL V3 book again, the following realization occured:
I am looking all through, from the point of view of the service provider. The confusion is created in my mind, because of this view point.
If you really look from the customer/business point of view, there is absolutely no ambiguity!. There is clear seggregation and one can clearly distinguish and categorize the IT service provider (who is serving that business) into one of these three categories.

Now looking back- the confusion looks a silly one, but I know how important it was, to get into this right perspective!!!

The realizaton happened when I noticed two specific things in the ITIL book:
a) The diagram which represents the external service provider – fig 3.14 in Service strategy.
b) The section title immediately after that which reads: “How do customers choose between the types?”

Yes, that is the whole thing: Business/customer perspective!