Learn English – it is shipped or has been shipped

Let's start by cleaning up your terminology:

1. Present perfect passive: The order has been shipped.
2. Present perfect active: The order has shipped.
3. Present passive: The order is shipped.

These all have essentially the same meaning: somebody has packaged your order and put it in the mail or on a truck to be delivered to you.

The important difference between them is that

• in 1, the verb ship is transitive. The order is the 'Patient' of the verb, the entity which undergoes the action. Its ordinary active-voice form would require that the 'Agent', the entity which performs the action, be named and act as Subject of the sentence, with the Patient, the order, acting as Direct Object:

  _{Agent/Subject}We  _VbPrPfActhave shipped  _{Patient/DirObj}the order.

  When this sentence is cast in the passive voice with a BE+PaPpl construction, the Patient becomes the Subject and the Agent is omitted or expressed with a by phrase:

  _{Patient/Subject}The order  _VbPrPfPasshas been shipped  (_{Agent/PrepPhr}by us).

• in 2, the verb ship is intransitive. It is in effect a different verb, which represents shipping as an action performed by the Subject, and there is no Patient.

  _{Agent/Subject}The order  _VbPrPfActivehas shipped.

  This sort of construction, in which the Patient of the action is 'transformed' into its Agent, is sometimes called middle voice, because it expresses a semantic relationship between the verb and the Subject which lies somewhere 'between' active and passive voice. It is fairly common with verbs like wash and shave, where it has a reflexive sense: John shaves (himself), Cathy washed (herself); it also occurs idiomatically with verbs like cook and drive:

  A stew was cooking on the stove.
  Toyota's new suspension drives very well.

• in 3, the verb has the form of a simple present passive; but I think most native speakers would understand this as a predication: the Subject, the order acts as the 'Topic', the verb is the copula is, and shipped is an adjectival Predicate Complement describing the status of the order.

  _{Topic/Subject}The order  _VbPrCopulais  _PredComp{shipped / delayed / pending / in transit / complete}.

In this context, there's really no reason to prefer any of these over the others. In other contexts, however, your choice might be significant. These two sentences, for instance, have quite different meanings:

The new Toyota drives well. This is a statement about the quality of the car.
John drives the new Toyota well. This is a statement about John's ability as a driver.

Your understanding of the three phrases is not quite correct:

1. has gone to - there or on his way to;
2. has been to - someone has been there but he is on his way back; OR someone has been there at some point in the past and is now elsewhere
3. has been in - someone is still there; someone has gone there at some point in the past and is still there

So these statements:

1. Have you ever been to / in Greece? - Yes, it's a very beautiful country;
2. When did you last go to Canada? - I've never been to Canada.

You could say HAVE you ever gone to Greece and it would be correct

I have never gone to Canada is also correct I have never been in Canada, while it would be understood, might sound odd to some. In this sentence I have never been TO Canada, would be correct.