First of all the verse address the disbelievers and believers, as ibn Kathir for example gave this part of the surah the title "EXPLAINING THE DAY OF DECISION AND WHAT OCCURS DURING IT". However in this verse the false expectations of disbelievers have been rectified.
Imam ibn Kathir comments this verse as follows:
(And all things We have recorded in a Book.)
meaning, "surely We know the deeds of all of the creatures, and We have written these deeds for them. We will reward them based upon this." If their deeds were good then their reward will be good, and if their deeds were evil their reward will be evil.
Fakhr ad-Dyn ar-Razi in his tafsir explains the verse as follows -see here in Arabic- in more details:
In the following I'm translating from Arabic language, as these translations are of my own take them carefully!
قوله : ( وكل شيء أحصيناه ) أي علمنا كل شيء كما هو علما لا يزول ولا يتبدل، ونظيره قوله تعالى : ( أحصاه الله ونسوه ) [المجادلة : 6] واعلم أن هذه الآية تدل على كونه تعالى عالما بالجزئيات، واعلم أن مثل هذه الآية لا تقبل التأويل;
The statement: (But all things) means WE knew everything as it is a knowledge that does not pass away or change, and a counterpart of this is is (Allah had enumerated it, while they forgot it;) (in al-Mujadalah 58:6) And know that this verse indicates that the Almighty knows the details, and you should know that such a verse does not accept interpretation.
وذلك لأنه تعالى ذكر هذا تقريرا لما ادعاه من قوله : ( جزاء وفاقا ) كأنه تعالى يقول : أنا عالم بجميع ما فعلوه، وعالم بجهات تلك الأفعال وأحوالها واعتباراتها التي لأجلها يحصل استحقاق الثواب والعقاب، فلا جرم لا أوصل إليهم من العذاب إلا قدر ما يكون وفاقا لأعمالهم، ومعلوم أن هذا القدر إنما يتم لو ثبت كونه تعالى عالما بالجزئيات، وإذا ثبت هذا ظهر أن كل من أنكره كان كافرا قطعا .
This is because the Almighty mentioned this as a report of what he claimed of saying: (An appropriate recompense.) It is as if Allah the Almighty says: I am aware of all that they have done, and I am aware of the directions of those actions, their conditions and considerations for which they deserve reward and punishment. There is nothing wrong that I do punish them except of with as much as it is in accordance with their deeds, and it is known that this destiny is only completed if it is proven that the Almighty knows the details of the details, and if this is proven, it will appear that everyone who denied it was an absolute unbeliever.
قوله : ( أحصيناه كتابا ) فيه وجهان :
His saying: (We have enumerated in writing(or book)) has two sides:
أحدهما : تقديره أحصيناه إحصاء، وإنما عدل عن تلك اللفظة إلى هذه اللفظة لأن الكتابة هي النهاية في قوة العلم، ...
The first is: it stands instead of we have enumerated in a count, but he changed it from that word (count or enumeration) to this word because writing is the completion in the power of knowledge. ...
القول الثاني : أن يكون قوله : ( كتابا ) حالا في معنى مكتوبا، والمعنى وكل شيء أحصيناه حال كونه مكتوبا في اللوح المحفوظ، كقوله : ( وكل شيء أحصيناه في إمام مبين ) [يس : 12] أو في صحف الحفظة .
The second is: That his saying: (book) be immediately in a written meaning, and the meaning and everything that we have counted as if it is written in the preserved board (al-Lawh al-Mahfoudh), like in (and all things We have enumerated in a clear register.) (in surat Yassin 36:12) or in the registers of the guardian-angels.
Sheikh Taher Benachour in his at-Tahrir wa-Tanwir
التحرير والتنوير -see here in Arabic- regards this sentence as a transition between two contradictory passages:
اعتراض بين الجمل التي سيقت مساق التعليل وبين جملة ( فذوقوا ) .
This is an objection between the sentences that lead to the course of explanation and the sentence (so taste them) (78:30).
وفائدة هذا الاعتراض المبادأة بإعلامهم أن الله لا يخفى عليه شيء من أعمالهم فلا يدع شيئا من سيئاتهم إلا يحاسبهم عليه ؛ ما ذكر هنا وما لم يذكر ،
The benefit of this objection is to inform them that Allah does not conceal any of their deeds, so he leaves none of their bad deeds but holds them accountable for it. What was mentioned here (in earlier verses) and what was not mentioned,
كأنه قيل : إنهم كانوا لا يرجون حسابا وكذبوا بآياتنا ، وفعلوا مما عدا ذلك وكل ذلك محصي عندنا .
As if it was said: They did not seek reckoning, and they disbelieved our revelations, and did other than that, and all of this is counted among us.
I could quote some more tafsir books. But let us focus on your question:
As my references above agree is a reference to the deeds of all humans, be it believers or disbelievers.
Refers to the register of deeds in which all of our deeds are stipulated.
In Arabic refers to different things depending on the context, it is nowadays mainly used as a reference for "books", while it may mean letter, message or anything written too.