There aren't really any similarities between the two other than players putting down alternating black and white pieces on a board. There are lots of other games of this kind, like Checkers and Reversi. Hex is in fact unique because it has hexagonal tiles instead of square ones. It is also a very recent invention.

Both Hex and Go place a strong emphasis on forming connected groups of adjacent pieces placed alternately and then never moved -- isn't this a similarity not shared with the other black-and-white-pieces games?

(Even the similar terminology of "stone" and "ladder" seem to hint at a relationship.)

Both heavily feature stone connectivity. But where connecting your sides with a stone chain is the goal in Hex, connected stones sharing liberties is only used to define capture in Go, and the goal is instead to take the most territory.

I think, if you're familiar with go, this is an uncharitable reading of the question. The victory condition in this game is very directly analogous to a not-uncommon source of (sometimes-game-deciding) violence in go--two nearby weak groups where connection means a decisive victory for whichever player achieves it.

Having not played Hex, I can't say whether it's strategically similar (although just from the first couple of chapters, there are definitely similar concepts of important shapes and ladder breakers).

There was a variant combining Hex and Go which was popular (as these things go) on online abstract games sites a few years ago. Square board, capturing like in Go, but the goal is to connect sides like in Hex.

This game degenerated to "primitive Go" most of the time, because both sides blocking each other is easy on a square board, and at that point it's down to who has the most territory (most free moves to fill in their own areas without being captured.

I've played both on a modest level. I'd say that Hex, at the sizes we typically play at, is a lot like one big Go fight. I find it easier to look far ahead in Hex since pieces are never removed, ladders are (even) more common, and since non-overlapping templates ("miai" in Go) always connect you can build them together into huge parts of the board where you know you can connect.

Thank you for avoiding the straw man I inadvertently invited to. This was indeed how I meant the question.