Both are iron, so why does my carbon steel pan behave nothing like my skillet?

The line between the two is carbon content: above roughly 2% carbon by weight you're in cast iron territory, and most cookware cast iron sits somewhere in the 2.5 to 4% range, while carbon steel pans are down around 1% or less. That extra carbon can't all stay dissolved in the iron, so in grey cast iron it comes out as graphite flakes threaded through the metal: and those flakes are why cast iron is brittle and cannot be forged or pressed thin. It has to be poured into a mould, thick. Steel with far less carbon is ductile, so it can be rolled and pressed into a 2 mm pan, and that thickness difference is most of what you feel every morning.

The practical consequences are worth knowing. Cast iron is brittle, so thermal shock cracks it - cold water into a screaming hot skillet is how people snap them. Carbon steel is ductile, so the same abuse warps it instead, and a warped pan spins on a glass hob but still cooks. Seasoning chemistry is identical on both, but the steel's thin walls get hotter faster at the rim, which is why wok users burn seasoning off the sides constantly and skillet owners rarely do.

I'd push back on 'it's all thickness'. Surface finish matters a lot in the first months. Sand-cast iron has a pebbled texture with real tooth for oil to key into, so early seasoning grabs unevenly and looks patchy exactly like yours describes. Rolled steel is smooth, so the first layers go on thin and even and look better sooner. Ten years in they converge, but your patchy-versus-even observation is about how the surface was made, not about carbon.

More carbon, more graphite, more brittle, has to be thick. Less carbon, ductile, can be thin. Everything you're feeling comes from that.

I found out about the brittleness the expensive way. Deglazed a very hot skillet with cold tap water, heard a crack like a dropped plate, and there was a hairline running from the cooking surface to the rim. It still technically worked and it wept oil onto the hob every time. Warm water, always.