I watched another person write something like this:
"A good segway makes the subject change seem like a natural extension of the discussion"
It's 'segue'. A good Segway does not involve subject changes. It involves rolling across pavement. The word you're looking for is 'segue'. SEGUE!
Ever since the segway came out, it's been a synonym for segue. It irritates me not because it's some company trademark co-opting the English language, it is because the two words are not interchangeable. For instance, if I ask for a Coke, a Coke is a type of soda, so using Coke as a synonym for soda is acceptable. Or if I remark that his head is as big as a Buick, a Buick is a type of car. Saying 'his head is as big as a car' is essentially the same as saying 'big as a Buick' (although there are multiple definitions of 'car', but you know what I mean). Noun-wise, they correspond somewhat.
Segue and Segway, though, are not related. One describes a vehicle and the other describes an aspect of conversation or writing. Here's a good example: 'He was arrested for dealing crack' and 'You cracked me up' are not similar. 'I sat on the chair' is not similar to 'today is saturday'. 'Bag' is not a synonym for 'Baguette'.
It probably, and this is speculation on my part, has to do with the look and sound of the word. Segue looks weird and sounds awkward. Slap a 'way' at the end and it's much easier to pronounce. It flows better. I'm not an expert in language, but that's how it feels to me.
So please remember: it's segue when you're talking in conversation. It's segway when you're riding the novel 'people mover'.