I don't want to call that idea simplistic because that seems rude, but you are right that it's more nuanced than that idea makes it out to be.

First of all, while there are a lot of similarities between Rhodesia and South Africa's treatment of its nonwhite peoples, their governments and overall strength were in substantially different places. Rhodesia's government existed illegally, and it never won formal recognition from any other government on the planet, even from South Africa and Portugal (its closest allies). In a country of around six million people, Rhodesian whites never numbered more than 300,000, and those numbers trended strongly downward over time. While its economy was strong through the early 1970s, it did exist outside of normal trade channels, and it depended specifically on South Africa and Portuguese control of Mozambique for access to outside goods. The Rhodesian Bush War has a slow start and doesn't really start to place serious pressure on the regime until the mid-1970s, but once the Carnation Revolution removed the Portuguese government from the region, it eliminates one of Rhodesia's allies while opening up a new hostile front in Mozambique, where rebels can go to safely lay their heads, in addition to enclaves elsewhere.

By contrast, South Africa was in a much more stable position in this period. After '63, the ANC and PAC's members have either fled, been imprisoned or killed, or have been driven so deeply underground that they can't effectively operate anymore. Furthermore, South Africa's government is a legally recognized one, even among other states such as the Scandinavian states that publicly commit and support opposition to apartheid. Its economy grows very rapidly from '63 until the oil crisis, and at least until the Carnation Revolution, it's surrounded by a cordon of friendly states.

Beyond their different political realities, the two governments are working toward very different goals. Apartheid became increasingly about the goal of "separate development" from the 1950s onward, which meant not just racial separation, but the eventual creation of tribal areas (Bantustans) that would legally be their own separate governments. Black South Africans might work in white South Africa, but otherwise, they would have their own separate spaces (while discrimination would be maintained against Indians and Coloureds).

The Rhodesians or at least Ian Smith thought in less all-encompassing terms; they wanted a settlement of some kind that would preserve white domination in Rhodesia but that would at least give the appearance of recognizing the needs of non-whites. Practically, this meant the "qualified franchise," in which a set percentage of blacks would have the vote and a set number of seats in parliament. However, Smith and others feel that they need to negotiate from a position of strength, partly to prevent a defection of right-wing Rhodesian whites, and partly because they were unwilling to accept a settlement that might seriously challenge white domination, only doing so when they were backed into a corner by circumstances.

South Africa's leadership goes on a diplomatic offensive in the same period. John Vorster succeeded Hendrik Verwoerd and was much more interested in a sort of accommodation that would serve apartheid. Part of this was an attempt to win support even in Black Africa through economic aid, and while it ultimately came to relatively little, there was not-inconsiderable optimism among Afrikaners that they could win legitimacy for their system. Offering concessions such as erosions of so-called petty apartheid allowed on the one hand, to try to win over black moderates in South Africa, and on the other hand win friends abroad.

Of course, those concessions were marginal when looked at very closely: the absence of political rights, the Group Areas Act, and others all remained in place. Even some of the economic concessions that permitted black South Africans into more skilled work was simple necessity: in a rapidly developing economy that needed skilled workers, there simply weren't enough white South Africans. The rhetoric of separate development makes it sound as though it was a concession to give black South Africans their own land and that it was in its own way multicultural, but of course the land that they received was some of the least arable in the country, and the so-called homelands were economically backward in the extreme.

White Afrikaners were also not of one mind; many were uncomfortable with the position of relaxing apartheid even superficially. This is one of the problems Vorster faced as PM, and Jamie Miller makes the case in An African Volk that PW Botha was able to operate with a striking degree of independence in providing aid to UNITA and the FNLA and in general militarizing South Africa to an even greater degree. Botha supported reform, too, but concessions were a way to preserve apartheid, not to undermine it. It's Botha who favored giving Coloureds and Indians certain political rights, but as a way of removing one source of opposition to apartheid.

Also, while the ANC remains open to the possibility of peaceful settlement, in the wake of Sharpeville it had effectively endorsed violent struggle as well. The fact that violence from the liberation movements was limited after 1963 was as much due to the fact that they simply were in a poor position to wage guerrilla warfare; even attempts to fight the Rhodesians alongside Zimbabwean nationalist groups didn't lead to successes on the battlefield for Umkhonto we Sizwe (the armed wing of the ANC). It picks up for MK after 1976, but that's another story.