These are the state income tax rates; Federal income taxes are on top of that. The bottom Federal rate is effectively zero, and tops out at 35% for marginal income over about $380K.
But the total tax bills are still not that different, as they are marginal rates for the most part and the threshold where they start are different.
The effective rate paid in the UK is still somewhat higher for most earners, but for most people it's not as much as you might think from just looking at the headline rates.