The MT for the Christian verse numbered Isaiah 9:6 is Isaiah 9:5:
כִּי יֶלֶד יֻלַּד לָנוּ בֵּן נִתַּן לָנוּ וַתְּהִי הַמִּשְׂרָה עַל שִׁכְמוֹ וַיִּקְרָא שְׁמוֹ פֶּלֶא יוֹעֵץ אֵל גִּבּוֹר אֲבִי עַד שַׂר שָׁלוֹם
The verse describes an event in the immediate past. It is an announcement of a news event that has just now happened. The following verse, regarding the child's name refers to a future event.
The problem with translating "a child is born to us" is that this isn't English usage. In fact, without this verse, it wouldn't be clear what "a child is born to us" means. It sounds like an ongoing event in the immediate present, which is not the way that we speak about birth in English.
Another problem with this translation is that in English we don't generally speak of a "child" being born, we speak of a "son" or "daughter" or "baby" or possibly "infant" being born. We generally use "child" for a later stage of life. In Hebrew however, the word ילד used in this verse, can mean either a newborn or an older child, depending on the context.
The translators use "male child", injecting the word "male", which isn't in the MT at all, but is inferred from the gender of "child", ילד, and which is clear from the parallelism of the next clause, "a son has been given us". The translator is forced into this situation because there is no clear synonym in English for "son" used in the parallel clause.
It is not possible to understand this verse without taking into account the alliteration and the poetic rhythm. The transliteration the verse is:
Ki yeled yulad lanu, ben nitan lanu, wa t'hee hamisrah al shichmo; ...
The prophet has chosen his words for maximum alliterative and rhythmic effect, like a chant used by demonstrators in a demonstration1. It is not possible to translate this effect without deviating significantly from the meaning of the verse.
So, to translate the meaning of the first half of the verse into modern American usage:
For a son has been born [to the Davidic line], a boy has been born, and the leadership will be on his shoulders...
In this translation I have indicated interpolations in brackets. It is clear from the context that the phrase לנו, translated as "for us" or "to us" refers to the the Davidic line, which is "our" (the prophet's audience) line of leadership.
Remember that the MT here is poetry and the translations that you are reading are translations of poetry that capture the gist of the meaning of the original but not the nuance, the rhythm or the alliteration. This means that when you compare translations you need to understand them as approximations of the translated text which means that you can't make theological inferences about the meaning of the original text based the translation. You also need to be aware of the translation philosophy of each translation. Some translations, like the KJV, probably sounded stilted in their time, because the translation philosophy was to stay as close to the Hebrew word count and word order as possible, in keeping with the Scholastic ideals of the period. Modern translations tend to value closeness to current idiom as the criteria for translation.
So, to answer the OP question, there might be a difference between "is born" and "has been born" in English, but it is not reflected in the MT. Both of these translations are reasonable.
- A similar example of slogan-like verse can be found in Isaiah 8:10, עצו עצה ותפר דברו דבר ולא יקום כי עמנו אל, ootsu aytsa watufar, daberu davar walo yakum ki imanu el.