Both are in the Solanaceae family, but how did they both end up as ATOes?
A little bit of “no reason at all,” and a little bit of human nature.
They share absolutely no etymology. Tomatos were called “tomates” before the spelling and pronunciation drifted – and it just kind of drifted into being very similar to “potato,” probably because people have a tendency to spooje things together.
There’s no rationale for it – it’s just the same as the tendency for people to pronounce “nuclear” as “nucular” – the ending is more familiar. We might find some weak connection between the concept of “molecular” and “nuclear” to explain the drift, but really it’s just that it’s easier for people’s tongues to use one string of motions for the bulk of both words than two.
If you’re constantly talking about tomates and potatoes, it’s kind of natural that the similarities are emphasized and the distinctions are blurred, until over time you’ve got tomatoes and potatoes.
Not in Australia they’re not. One is Tom-AH-toe, the other Pot-ATO. 
Aww, let’s call the whole thing off!