They mean the same thing. One is the past participle as the adjective (a package that is shipped) and the other is the past perfect passive (a package that has been shipped)
You can do this sort of thing with many English verbs:
A meal that is eaten / a meal that has been eaten
An exam that is completed / an exam that has been completed
A question that is left unanswered / a question that has been left unanswered
Sometimes one sounds better than the other. Example:
Once the car is started, check the oil pressure again.
Here you can say once the car has been started, but with things like instructions, it's common to use simple, direct statements.
Again, there is no difference in meaning, so which you choose is usually up to personal writing style. Unfortunately I can't offer any rule to help choose which, except to say that the past perfect passive should be fine, if you can't decide.
Note that both of these are passive constructions. The subject causing the action is not as important as object being acted on, and is often omitted.
Once the new rules are submitted / have been submitted to the committee, they can be debated.
The passive voice allows us to avoid specifying who is submitting the rules, either because it's not important information, or because the writer doesn't want to say:
Let's just say that the window has been broken, and the cost of its repair will be paid by the person responsible.
Best Answer
Let's start by cleaning up your terminology:
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:
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:
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.
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:
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.
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: