Hajj and Umrah are some of the most significant acts of worship in Islam. Both are unique in their performance, as unlike other worship, these cannot be performed outside of Mecca; one has to travel to the Ka'aba, situated in Mecca, Saudi Arabia. While Hajj can be performed only on specific dates, from the 8th to 12th/13th of the Islamic month of Dhul-Hajj, Umrah can be performed at any time of year.
However, both of them can only be performed in Mecca, not elsewhere. Although there are some basic rituals, which are the same for both Hajj and Umrah, they are different in many ways.
Hajj is obligatory for those adult men and women who possess sufficient financial resources to travel to Mecca and are physically capable of performing the Hajj rituals. More importantly, it is obligatory only once in a lifetime. However, there is no restriction on performing it multiple times; if one intends to do so, the scholars recommend avoiding it.
Hajj is one of the five pillars of Islam, often placed at number 5, after faith in Oneness of Allah, سُبْحَانَهُۥ وَتَعَالَىٰ, Prayers, Zakat, and fasting in Ramadan. The five pillars of Islam are specifically mentioned in many Hadiths, which can be found in almost all the major authentic Hadith Collections, such as Hadith 16a of Sahih Muslim.
Translation - (The superstructure of) al-Islam is raised on five (pillars), i.e., the oneness of Allah, the establishment of prayer, payment of Zakat, the fast of Ramadan, and Pilgrimage (to Mecca). A person said (to 'Abdullah b. Umar, the narrator): Which of the two precedes the other-Pilgrimage or the fasts of Ramadan? Upon this, he (the narrator) replied: No (it is not the Pilgrimage first) but the fasts of Ramadan precede the Pilgrimage.
The obligation and significance of Hajj are specifically mentioned in the Quran on many occasions, such as the 96th and 97th verses of Surah Al-e-Imran.
Translation
Similarly, the obligatory nature of Hajj and its importance are also mentioned in the 197th verse of Surah Al-Baqarah.
Translation - Known are the months of pilgrimage. If one resolves to perform the pilgrimage in these months, let him not indulge in concupiscence, sin, or quarrel. And the good you do shall be known to God. Provide for the journey, and the best of provisions is piety. O men of understanding, obey Me.
In addition to mentioning the virtue of performing Hajj, its etiquettes are also narrated here, such as avoiding indulgence in sin and fighting during the month of Hajj.
Umrah, which translates to “to visit”, refers to visiting the Ka'aba. It is known as the shorter version of Hajj, comprising only some of the basic rituals, such as Tawaf (circumambulating the Ka'aba) and Sa’i (briskly walking between the hills of Safa and Marwa). Both these rituals are required to be performed seven times each. Unlike Hajj, Umrah can be performed at any time of year, but one must travel to Mecca to perform it.
Performance of Umrah is mentioned in the Quran alongside Hajj, in the 196th Verse of Surah Al-Baqarah.
Translation of relevant part - Perform the pilgrimage and holy visit ('Umra, to Makkah) in the service of God
The performance of Umrah might be convenient for someone who otherwise might not be capable of performing the complete Hajj. Some of the reasons might be:
Although not obligatory and a shorter form of the Hajj, it offers significant rewards and is considered highly virtuous. The virtues of Umrah are mentioned in many Hadiths as a rich source of expiation of previous sins. Moreover, in certain conditions, it is also considered equal to Hajj.
Hadith 1773 of Sahih Al-Bukhari narrates that sins are expiated through the performance of Umrah.
Translation of relevant part - "(The performance of) `Umra is an expiation for the sins committed (between it and the previous one).
Although Umrah can be performed during any Islamic month, it is considered highly virtuous if performed during the month of Ramadan, as mentioned in Hadith 1863 of Sahih Al-Bukhari.
Translation - When the Prophet (ﷺ) returned after performing his Hajj, he asked Um Sinan Al-Ansari, "What did forbid you to perform Hajj?" She replied, "Father of so-and-so (i.e. her husband) had two camels and he performed Hajj on one of them, and the second is used for the irrigation of our land." The Prophet (ﷺ) said (to her), "Perform `Umra in the month of Ramadan, (as it is equivalent to Hajj or Hajj with me (in reward)
In short, both Hajj and Umrah are highly virtuous and hold a significant status in Islamic worship. If one can afford both physically and financially, he/she must fulfill this religious obligation, but doing so repeatedly, just to show one's status in society, is not recommended. It should be avoided. More importantly, before proceeding to Mecca for the performance of Hajj or Umrah, one must learn how to perform various rituals correctly, at the correct timings.