In short - The Boer people are people who fled Europe to escape the Christian persecution, where between 65 and 69 million people were slaughtered, burned alive and tortured to death by the Christians who wanted to force everyone into their faith.  Therefore, when the opportunity arose, many fled to the USA, and others to the Cape in Southern Africa.
 

These Europeans were known as Free Burghers because they were rejected by their own countries, and fled from country to country to escape the Christian killings, and therefore had no motherland of their own.  They were therefore not citizens of a country.
 

Upon arrival in the Cape, the Christian Cape Dutch were there, who were colonialists (Dutch citizens), who were sent to supply food to the ships on the food route to the East.  These Dutch could not farm, and therefore the British VOC society offered the opportunity to the Vryburgers on the condition of the Vryburgers that they would not be dominated by other authority.  This is what the Cape Dutch tried, as well as trying to force the Free Burghers into their Christian faith, which caused the Free Burghers to settle outside the colony's borders.  The Vryburgers were also known as Border Farmers.
 

About 50 years later the British annexed the Cape and together the British and the Cape Dutch made the life of the Border Farmers hell.  When circumstances became unbearable, they decided to flee again from the oppression, and the Great Trek began.

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The nickname BOER became the identity of the Boer people, a people formed on African soil, and which is indigenous to Southern Africa.

The Boer people are not Dutch, they formed a unique people from mainly Germans, also Dutch and other Europeans, with their own tutonic language (referred to as 'the Language') Boers.
 

The Cape Dutch (today Afrikaner) did not take part in the Great Trek.

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After several attempts to establish a Republic, which were repeatedly thwarted by the British and Cape Dutch Afrikaners, the Boers succeeded in establishing the Transvaal Republic (ZAR) and gained international recognition for it on 17 January 1852 during the Sand River Convention.  Two years later the Free State was internationally recognized at the Bloemfontein Convention on 23 February 1854.
 

  The Boer people do not accept domination by foreigners and reject the British, the Afrikaners, and any African group that wants to exercise authority over the Boer people.

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Under the Vow of Blood River to the Creator of Heaven and Earth, we may not mix with other races, religions, and political structures.​
 

References:
http://markhumphrys.com/christianity.killings.html#crusades Killings for Christianity