Bush War is a predominantly late-colonial term used almost solely by the white populations of African states, that fundamentally refers to the fact that the nature of the combat in these conflicts was rural (i.e. fought in the bush or countryside) as opposed to urban, and the implication is also that the war involved guerrilla tactics rather than large-scale, pitched battles (although there were exceptions to this assumption).

The term itself was created during the wars and was designed to both misleadingly reassure populations as the the small-scale of the combat (Bush War sounds much better than a War of Liberation or Resistance War or Civil War) and to reaffirm the legitimacy of the ruling government within the conflict.

However, all of these conflicts are more properly referred to by other terms for a variety of reasons, not least the fact that the term Bush War was purposefully misleading and often misrepresented what the war was actually about - the Angolan Bush War is legally defined as the South African Border Wars by the South African government, but ask any veteran or citizen how they would refer to it and Angolan Bush War is the popular term. The term Bush War has been neglected by academic historians due to the reasons above and the connotations (perceived or real) that come with the terminology of the colonial settler states.

For example, with regards to the Rhodesian Bush War, the more common terms now used are the War of National Liberation in Zimbabwe, or Zimbabwe's Liberation War (or in Shona, the Second Chimurenga). Following the change from white minority rule to independent majority rule in 1980, the new African nationalist state rejected the colonial terms such as Rhodesia, Salisbury, and Gwelo (for example), and renamed them with the preferred and mostly historical African identifications of Zimbabwe, Harare and Gweru. Similarly, the term Rhodesian Bush War has become more colloquial in usage and seemingly identified with the white Rhodesian population - the main places you will see it used is in academic work from the 1960s, 70s, and early 1980s, the memoirs of white Rhodesians (for example Dennis Croukamp's The Bush War in Rhodesia), and finally the persistent online-forums that praise the Rhodesian Bush War as being the shining beacon of how an anti-insurgency war should be fought (never a good sign as to who uses a term).

Anyhow, tl:dr is they are called Bush Wars for the fact combat took place in the Bush, and because it was less disturbing to (mostly white) populations to think of them as Bush Wars rather than Wars of Liberation. But they are usually given different names in academic work!

edt: can't believe I forgot to mention this article - this actually makes the arguement that a Bush War is a specific type of warfare, unique to Africa and typically involves what could be called 'low-intensity' strategies (as in, guerrilla warfare).

"Bush" in ex-colonial English terms is "countryside".
(Think "Jock of the bushveld") Typically these wars are fought in the open areas of the country and not in the cities, with training camps, insurgent routes and arms caches being hosted in the "bushveld".

The national armies involved in these were typically fighting their own people who had foreign assistance.
Unlike a civil war, fought primarily in cities between civilian groups, these were typically between state forces and rebels. (South Africa, Rhodesia)

In the case of Angola-South Africa bush war, Angola had Cuban assistance.
The South African strikes into Angola were to attempt to neutralise Angolan threats of assistance and SWAPO (south west Africa peoples organisation) training camps hosted in Angola.

With the exception of a few instances, most of those actions took place outside urban areas, in the "bush".