This area can be complicated for the philatelist. Technically the British South Africa Company should not be listed under Rhodesia, it should be under its own heading. At it's height, it covered an area of what is now Zimbabwe and Zambia.
Here is a chart of the historical divisions.
Note that British South Africa Company Stamps were used in Southern Rhodesia until 1923, and Northern Rhodesia until 1924. Then they got their own stamps.
With the unification in 1953, all three territories used stamps inscribed Rhodesia & Nyasaland.
When the Federation collapsed in 1963, they all issued stamps again, then after independence, they all issued more stamps under their new names.