Thinking about it more, I could see saying sitting "in" a chair if it had an extremely-high back and sides, so it was sort-of enclosing you. But I'd always sit "on" a regular chair or a bench.
In/on is a hard distinction for some non-native English speakers; even native speakers have trouble explaining how we make the choice (for instance, we say "on the bus" even though we're inside it, possibly because historically, omnibuses were open, and the phrase stuck after they got sides, roofs, and motors replaced the horses; that also applies to other public transit, like trains, planes, ships, etc. If you say "in the bus" you're making a special emphasis, e.g. "three victims are still in the bus.").
It's not so hard. In French we say s'asseoir sur une chaise (to sit on a chair), but s'asseoir dans un canapé (in a sofa), dans un fauteuil (in an armchair). So it's a natural distinction.
For the "on bus", I think it's rather related to the "on board", as we say "on train", "on boat", etc...
Aboard: The etymology is from the French "à bord".
The "à" in "à bord" means the motion, and "bord" represents the ship/train/travel engine. So it means getting in the "travel machine", whatever it is. (bord = edge of the boat, so the opposite side of the edge of the boat)
On board and aboard are related, and have only a difference of preposition in their meaning, but it would take too long to explain or discuss it here.
Where I come from the two are used interchangeably, however on tends to be used for wooden or plastic seating. Harder surfaces with little to no give when you sit. In would be used more for armchairs, sofas, etc. Softer seating that would sort of sink in when you sat down. Both would be understood to mean the same thing.