Difference between "was already" and "has already been"

Both sentences are in the passive voice, meaning they use indirect construction. The only difference between them is that between the "present perfect tense" and the "preterit tense."

The package has already been received.

The above uses the present perfect tense: has been. The present perfect tense is formed with a present tense form of "to have" plus the past participle of the verb, which in this case, being passive voice, is both "been" and "received." This tense indicates either that an action was completed (finished or "perfected") at some point in the past or that the action extends to the present.

The package was already received.

The above uses the preterit tense: was. The preterit tense or simple past indicates that an event was completed in the past. Being in the passive voice, "was" combines with the past participle "received."

The choice between present perfect and preterit is often determined by the adverb accompanying the verb. With adverbs referring to a period gone by, we would use the simple past:

• I studied all night/yesterday/on Wednesday.

With adverbs beginning in the past and going up to present, we would use the present perfect:

• I have studied up to now/lately/already.

An adverbial time-marker such as "today, this month," or "for an hour" can take either the simple past or present perfect:

• I worked/have worked hard today.

We tend to use the present perfect when reporting or announcing an event of the recent past:

• The company's current CEO has lied repeatedly to her employees.

But we tend to use the preterit when reporting or announcing events of the finished, more distant past:

• Washington encouraged his troops.

Because the time limits for present perfect are relatively elastic (stretching up to the present), it is somewhat less definite than the preterit:

• Brett has worked with some of the best chefs of Europe [in the course of his long and continuing career].
• Brett worked with Chef Pierre LeGout [when he lived in Paris].

(Notice how the topic of Brett's work is narrowed down as we move from Present Perfect to Simple Past.)