Rhodesia tends to refer to the old colony of Southern Rhodesia - a British Central African colony. Southern Rhodesia separated from Northern Rhodesia in 1910 and became a Crown Colony in its own right.
The Northern bit was administered by British South Africa Company charter between 1911-1924, before becoming a British Protectorate - a status that lasted until 1953. Northern Rhodesia became federated with Nyasaland and Southern Rhodesia between 1953-1963 as the Federation of Rhodesia & Nyasaland before this arrangement dissolved a decade later in 1963. Northern Rhodesia became independent as Zambia the following year, as did Nyasaland, which became Malawi.
Southern Rhodesia regained its colonial status upon the federal break up, but this short-lived tenure lasted a year before Ian Smith declared Unilateral Declaration of Independence (UDI) in 1965 and dropped the 'Southern' prefix.
UDI was a result of the Rhodesian administration refusing to be cowed in to submission by the British Labour government over the issue of black majority rule. Ian Smith pointedly refused to allow this to happen, knowing (quite prophetically) full well what the result would be.
Rhodesia - despite not having a system of apartheid - became somewhat of a pariah state on the international scene and sanctions were imposed. This could have been quite disastrous, as Rhodesia was engaged in a counter insurgency war in the bush with Marxist rebels. But the Rhodies were an industrious lot and circumvented the arms embargoes by using some ingenious and downright dirty methods of arms acquisition.
Rhodesia became a republic in 1970 and severed its ties with the 'mother country' in totality. It continued to fight its war of survival against various factions (ZANLA, ZIPRA etc.) for another decade before finally being forced around the negotiating table at Lancaster House. Many Rhodesians saw this as a sell out to the 'Commies'. They weren't wrong.
Rhodesia briefly returned to colonial status during the brief period before becoming Zimbabwe in 1980, and a whole new chapter of heartache began in this once stable colony of the British Empire. It also proved that sometimes colonisation is not such a bad thing after all - especially when weighed up against the alternatives.