Two types of spirituality

In the Catholic Church, there are two major directions of spirituality. Probably, these two approaches are shared by other Christian traditions as well. On one hand, there is an active approach. This is exemplified by Martha. She worked busily to serve the Lord. The other approach is a relatively passive one. This is exemplified by Mary, the sister of Martha. The story is found in the gospel of Luke 10:38-42. Jesus praised Mary. Therefore, the Catholic Church also favours the passive, contemplative approach.
Roughly speaking, the aim of spirituality is to cultivate a close relationship with God. The active approach takes spirituality in our own hand. We do a lot of spiritual activities such as saying prayers, attending masses, going to retreat, taking part in Spiritual Exercises etc. in order to enhance our spirituality, our relationship with God. Following the teaching of Matthew 25:40, we also perform charity works to serve Jesus. This is the Catholic tradition of corporal and spiritual works of mercy. There are 7 corporal and 7 spiritual works of mercy. They are:
Corporal works of mercy:

1. to feed the hungry
2. to give drinks to the thirsty
3. to clothe the naked
4. to harbour the harbourless
5. to visit the sick
6. to ransom the captive and
7. to bury the dead.

Spiritual works of mercy:

1. to instruct the ignorant
2. to counsel the doubtful
3. to admonish sinners
4. to bear wrongs patiently
5. to forgive offences willingly
6. to comfort the afflicted and
7. to pray for the living and the dead.

With the passive approach, we enter into a state of rest through prayers and let God takes control over our spirituality in His hand. Usually, this is the mystical stage of prayers which many of us seldom reach because it is beyond our control. God, in His pleasure, touches us with indescribable peace and bliss.
Probably, this is what the authors of Psalm 95 and Hebrews mean by "God's rest". The author of Hebrews understands God's rest from Genesis. After six days of Creation, God rested on the seventh day from all His work (Hebrews 4:4b, Genesis 2:2). Making use of Psalm 95:11, he shows that the Israelites have failed to enter God's rest because of their lack of faith and disobedience.
For good news came to us just as to them; but the message which they heard did not benefit them, because it did not meet with faith in the hearers.
For we who have believed enter that rest (Hebrews 4:2-3a).
The author of Hebrews reassured Christians that they were able to enter God's rest because they believed and held fast to this belief in Jesus. Why did he believe that Christians had this opportunity to enter God's rest? He based his argument on Psalm 95:7b. He pointed out that the promise of God's rest was still open to us (Hebrews 4:7-9).
It is interesting to notice that when the author of Hebrews quoted Psalm 95:7b-11 in chapter 3, the quotation occupies the same verse numbers! Here in chapter 4, when he quoted Psalm 95:7b again, it is in Hebrews 4:7b! Remember, at the time he wrote this epistle, the verse numbering system had not yet invented! His hand must have been guided by God.

Dear Lord, may we treasure this opportunity You open up for us to enter Your rest. Let us hold fast our hope and faith in You and do not disobey You. Amen.

Appendix:
And God rested on the seventh day from all his works
καὶ κατέπαυσεν ὁ θεὸς ἐν τῇ ἡμέρᾳ τῇ ἑβδόμῃ ἀπὸ πάντων τῶν ἔργων αὐτοῦ (Hebrews 4:4b)
καὶ κατέπαυσεν τῇ ἡμέρᾳ τῇ ἑβδόμῃ ἀπὸ πάντων τῶν ἔργων αὐτοῦ. (Genesis 2:2).