I feel like Ironborn are very different than First Men in multiple aspects. As the books suggest, First Men when explored Westeros starting from South to North, some of them discovered Iron Islands and lived there, which then later got called as Ironmen but a lot of things contradict with this assumption.
First of all, after the initial fights with Children of the Forest (CotF), First Men started believing in the Old Tree Gods. And since Iron Islands are too rocky for weirwoods to grow, no Tree Gods were present there; no roots no presence. Why would they just forget their Old Gods? Isn’t that a little against their belief system? How did the Drowned God suddenly came into picture? I don’t recall any instance of that in their legendary tale of The Grey King.
Maesters believe the contradiction of the Seastone chair is just an exaggeration of the First Men but that doesn’t mean it can’t certainly be disregarded. The Maesters were among the Andals while the First Men didn’t have the ability to write and read, so it might as well be true. That a different species but close in evolution with First Men were already living on the Iron Islands before First Men came, and so the Seastone chair.
Also what about the difference in cultural aspect? Ironborn say they don’t sow. This goes totally against First Men who always sow. Sowing is part of their belief system about taking care of trees. Even the ideology of political system are different. The sons of the The Grey King decided to held a Kingsmoot; that’s basically a form of flawed democracy which is super different than the full Monarchial system for First Men, where bloodlines held the power to rule. Think about the way they name their castles. Pyke on Pyke, Harlaw, Orkmont. Why would they name their castles based on their names? Winterfell, White Harbour, Moat Caitlin; they aren’t named like that. Seems like culturally different way of naming castles and other things.
These were just on top of my head but there are multiple different categories in which they can be differentiated. Iron Islands is such an interesting place for a historian.