Everything that reaches us of good things and blessings is from the provision of Allah, whether we earn it with our own hands or someone else gives it to us as a gift
Question

I understand Rizq is written for us with Allah. What is considered under the category of rizq? Is it just the money we make on our own with our own time? Or can it also be money a relative gives you as a gift? Is that also considered part of my written rizq?
Praise be to Allah.One of the beautiful names of Allah, may He be exalted, is ar-Razzaaq (the Provider). Allah, may He be glorified and exalted, says (interpretation of the meaning):
{And I did not create the jinn and mankind except to worship Me.
I do not want from them any provision, nor do I want them to feed Me. 
Indeed, it is Allah who is the [continual] Provider, the firm possessor of strength} [adh-Dhaariyaat 51:56-58].
Ar-Razzaaq is an emphatic form of the active participle az-Raaziq (provider); what is meant is one who gives a great deal.
Everything that Allah decrees for His slaves and sends down to them from His stores, whether that is wealth, children, a wife, knowledge, a good appearance, or sound health… all of that comes under the heading of the provision that Allah grants to His slaves, whether that is what they earn with their own hands, or an inheritance that they inherit, or a gift that reaches them, and also whether that is from a halaal or haraam source. All of that comes under the heading of the provision that Allah grants to His slaves.
Allah, may He be exalted, says (interpretation of the meaning):
{And in the heaven is your provision and whatever you are promised} [adh-Dhaariyaat 51:22]
{And whatever you have of favor - it is from Allah} [an-Nahl 16:53].
The Prophet (blessings and peace of Allah be upon him) described whatever wealth reaches a person from someone else as provision (rizq). It was narrated from Abu Hurayrah that the Prophet (blessings and peace of Allah be upon him) said: “Whomever Allah grants anything of this wealth without him asking for it, let him accept it, for it is provision (rizq) that Allah has sent to him.” Narrated by Ahmad (7908); classed as saheeh by al-Albaani in Saheeh al-Jaami‘ (5921).
It was narrated from al-Qa‘qaa‘ ibn Hakeem that ‘Abd al-‘Azeez ibn Marwaan wrote to ‘Abdullah ibn ‘Umar: Tell me of your need. ‘Abdullah ibn ‘Umar wrote back to him, saying: I heard the Messenger of Allah (blessings and peace of Allah be upon him) say: “Start with those who are your dependents, and the upper hand is better than the lower hand.” I think that the upper hand is the one that gives and the lower hand is the one that asks, and I am not asking you for anything, but I will not reject any provision that Allah sends to me through you. Narrated by Ahmad (6402); classed as saheeh by the commentators on al-Musnad.
Al-Bayhaqi (may Allah have mercy on him) said:
Abu Sulaymaan said, according to what was narrated to me from him: ar-Razzaaq is the One Who is in charge of granting provision, Who ensures that every soul will get what it needs of food.
He said: Everything that we receive from Him belongs to Him, whether it is permissible or not permissible, for it is the provision of Allah, in the sense that He is the One Who caused it to be nourishment and food. "Al-Asma’ wa’s-Sifaat (1/172)".
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
What is meant by the word rizq (provision) is what Allah, may He be exalted, has made permissible to a person and has granted to him.
It also means that which nourishes a person.
The former is as in the verses
{And spend [in the way of Allah] from what We have provided you} [al-Munaafiqoon 63:10]
{and spend out of what We have provided for them} [al-Baqarah 2:3].
This provision is that which is halaal and is owned by that person. It does not include alcohol and that which is haraam.
The latter is as in the verse:
{And there is no creature on earth but its provision is due from Allah} [Hood 11:6].
Allah, may He be exalted, provides for the animals, but it cannot be said that animals own their provision, or that Allah has permitted that for them in the sense of it being permissible according to Islamic teachings, because animals are not accountable for their deeds – just as children and the insane are not accountable. But in the case of animals, we cannot say that they own their provision or that things are haraam for them.
Rather what is haraam is some of that which may provide nourishment for people. This is part of the provision that Allah provides as nourishment, and He decreed that, unlike what He made permissible and enabled them to own it.
It is narrated in as-Saheehayn from Ibn Mas‘ood, from the Prophet (blessings and peace of Allah be upon him), that he said: “The creation of any one of you is put together in his mother’s womb for forty days as a nutfah (sperm-drop), then he becomes a ‘alaqah (a piece of thick coagulated blood) for a similar period, then he becomes a mudghah (chewed piece of flesh) for a similar period, then Allah sends to him an angel, who is enjoined to write down four things. It is said to him: Write down his provision, his lifespan, his deeds and whether he is doomed (to Hell) or blessed (destined for Paradise). Then the soul is breathed into him. By the One in Whose hand is my soul, one of you may do the deeds of the people of Paradise until there is nothing between him and it but a cubit, then the decree overtakes him and he does a deed of the people of Hell and enters it. And one of you may do the deeds of the people of Hell until there is nothing between him and it but a cubit, then the decree overtakes him and he does a deed of the people of Paradise, and enters it.”
The haraam provision that Allah may decree for a person and that the angels write down comes under the heading of what Allah has willed should happen and what He has created. Nevertheless, He has forbidden it and prohibited it, so the one who does it incurs of His wrath, condemnation and punishment what he deserves. And Allah knows best.  "Majmoo‘ al-Fataawa (8/545)".
And Allah knows best.