Well, my quote about Black Tern, 'rare with very few confirmed records' was from Birds of the Horn of Africa' by Redman, Stevenson and Fanshawe, which is the English-language main reference for the area. But it also says that it is 'recorded in most months' which seems to contradict this slightly.
The same book says that White-winged Tern is a 'very common passage migrant and winter visitor'. Whiskered Tern is 'locally common, but not numerous'.
I'm not at all an expert on these Marsh Terns, but they are notoriously difficult to separate in winter plumage, especially if you don't have experience seeing a lot of them. White-winged Tern used to be called White-winged Black Tern. Whiskered Terns which we have where I am seem to vary a lot in non-breeding plumage, and I thought Black and White-winged did too.
But MTem and KGS are undoubtedly much more experienced than me with these birds, and if they think this is Black Tern, then it may well be. If so, you were lucky to find it there.
When we were at Ziway in 2012, also in winter, we saw lots of birds in just a few hours, but no terns, just a couple of Black-headed Gulls. (We saw Whiskered Terns at Lake Tana.)
But if you were there five days, you may well have seen a lot more than us.
Did you see any other terns in that time? It would be interesting if you saw only one tern in five days, and it turned out to be the rarest.
I don't know about the site you linked to 'World Birds', but as far as I can see, it doesn't have 'White-winged Tern' in its list of birds at all (for any country). Nor does it seem to have 'Whiskered Tern'. And it mispells the binomial of Black Tern as Chilidonias. And its search function doesn't work well. So I would say it's not reliable at all. It looks like someone has 'scraped' some online source to make a website to make advertising money.
In my experience Wikipedia's list of birds by country are pretty reliable. Here is their
list for Ethiopia.