What happened to Botswana colonization?

The British, it was called Betchuanaland. Bechuanaland was never a colony as such, it was a "protectorate" of Britain. In a nutshell, the people of Bechuanaland requested British protection from the South African Boers, the British did not want the Boers or Rhodes, who at that stage was in Rhodesia, moving into Bechuanaland, so this was an arrangement that was beneficial to both the people of Bechuanaland and the British.