The Noble Eightfold Path for monks and for lay disciples?

It's not possible to follow the path outside the Brahmacaria, good householder. Practice for beyond starts with the Uposatha-observance.

And yes, this Ariya-magga, isn't one of on-house (stand)-holder, holder of the world, seekers of refuge in the senses, and requires to leave home to develop.

In regard of how deep "sex" actually goes to fit really into Brahmacaria, one may investigate and reflect the Methuna Sutta: The Discourse on Coupling (May one be aware that Upasaka Piya Tan couldn't let go of first and so the exolainings related to him are corrupt while else if fine, first version was actually better, before his total going back...)

And one cut's oneself totally off if revil the Tathagate, downvotes the truth of Dhamma and has no regard toward recluses... so it's total not the path for ordinary householder, consumer, used to wish, demand and go after the low first.

[Note that this isn't given for stacks, exchange, other world-binding trades but for escape from it]

Nobel Eight Fold Path is for the entire humanity. If you sincerely walk upon it you will become a monk and eventually you will attain Nirvana.

Lay followers engaging in the sexual act are not practising the Noble Path because they are not practising intention of renunciation of the 2nd factor, not practising celibacy of the 4th factor and not practising abandoning of lust, covetousness & sensual hindrance of the 6th, 7th & 8th factors.

The reason for such a distinction in translation is Bhikkhu Bodhi is simply totally wrong; like both he and Sujato are totally wrong about many things (although Sujato is not wrong on this occasion).

OP: Does it imply that lay followers still engaging in the sexual act while monks giving it up are both following the Noble eightfold path ? Or would there be yet a reason for such a distinction in translation?

Yes, it is true that there is indeed a separation of the path for lay followers and for monks. The former is the version with defilements, and the latter is the noble version without defilements i.e. the full-fledged Noble Eightfold Path for monks (and nuns) only.

The path of the lay follower who practises Right Action, Right Speech, Right Thought and Right Livelihood as applicable to lay persons, is a valid path in Buddhism, even if it is not THE noble path that leads to the complete end of suffering. I speculate that the lay follower path may not go beyond stream entry, due to lack of renunciation.

From MN 117 (translated by Ven. Sujato) regarding Right Action:

And what is wrong action? Killing living creatures, stealing, and sexual misconduct. This is wrong action.

And what is right action? Right action is twofold, I say. There is right action that is accompanied by defilements, has the attributes of good deeds, and ripens in attachment. And there is right action that is noble, undefiled, transcendent, a factor of the path.

And what is right action that is accompanied by defilements, has the attributes of good deeds, and ripens in attachment? Refraining from killing living creatures, stealing, and sexual misconduct (kāmesu micchācārā). This is right action that is accompanied by defilements.

And what is right action that is noble, undefiled, transcendent, a factor of the path? It’s the desisting, abstaining, abstinence, and refraining from the three kinds of bad bodily conduct in one of noble mind and undefiled mind, who possesses the noble path and develops the noble path. This is right action that is noble.

The word "abrahmacariya" is not used above.

This sutta contains similar dual versions for Right Speech and Right Livelihood. Interestingly, there's also Right Thought (with two versions).

After writing the above answer, I found that a wise lay follower can become an Arahant on his death bed in SN 55.54:

If they reply, ‘I have done so,’ they should say: ‘Good sir, the Brahmā realm is impermanent, not lasting, and included within identity. It would be good to turn your mind away from the Brahmā realm and apply it to the cessation of identity.’

If they reply, ‘I have done so,’ then there is no difference between a lay follower whose mind is freed in this way and a mendicant whose mind is freed from defilements; that is, between the freedom of one and the other.”

Ven. Thanissaro's commentary to SN 55.54 indicates that a wise or discerning lay follower in this sutta, actually refers to a lay follower who has at least achieved stream entry.