As a South African, I can confirm that Exhibit A is definitely referred to as chips, in fact, we also use the term slap chips, which means chips that are slightly soggy as they've been bathed in vinegar; so chips is definitely common usage. See this menu from Nandos, a South African company of some renown, which uses chips too.
Fries, on the otherhand, are also common usage, but tend to be generally more associated to American-style fast food chains as is shown here, although in common parlance the words are interchangeable.
Moving on to Exhibit B, I'll again reference a pre-eminent manufacturer of these comestibles, in this case, Simba. Simba refers to their product as chips too, and so this is common parlance for items shown in Exhibit B, especially given that Simba's market-share is arguably the largest for these products in South Africa.
The term crisps, however, is well understood, and is certainly used when differentiation between these products is necessary.