This is not a tax on income. As your citation says, it is a tax on going without health insurance. The authority cited by the Court is from I.8.1.
Ask yourself this. Suppose the 16th Amendment did not exist. Would this ruling have been any different? My answer is 'no'.
It's both.
Those without insurance pay a larger tax on their income than those with insurance.
The very same thing happens when some people don't buy solar panels for their house or they don't purchase educational services -- they will pay more income tax than those that get the deductions or credits for those purchases. Mathematically it's the same thing.
Politically, though, perception of the two is different. Congress didn't want to be seen as increasing taxes, though that's what they did. And they didn't want to be seen giving deductions, since their constituents would see that giving taxpayers a tax break.
But it isn't perception and deceptive language that matters when trying to come to a correct judgement. If someone calls a tax a "penalty" in order to fool voters, it doesn't change the fact that the thing being called a "penalty" is still a tax. A tax is as a tax does.