Taxes and tax terminology are quite a bit different in the US.
Gross income, take home pay (not exactly relevant for computing taxes), adjusted gross income, tax deductions, taxable income, taxes due, tax credits are all different concepts for individuals. To simplify matters, saying that companies and individuals pay taxes on net taxable income is fairly accurate without getting into all the messy details of the US tax code. In the US, taxes are not calculated on the basis of Gross Income.
Because only amounts over a certain level of income are taxed, and because of tax credits, and because some do not have any income, only about 50% of US households pay federal (or state) income taxes, In some cases they may actually get money back from the government (over and above any withholding) because of tax credits, primarily the earned income credit for low income persons who have a job that does not pay very much money (and especially if they have children they support).
And people in the UK complain about taxes being too complex, your system is way more horrible (by horrible I mean unnecessarily complex).
In the UK there are 2 basic types of income tax, they are simply "NI" (National Insurance), and "Income Tax", both of these vary by how much you earn, NI is a relatively small sum whilst Income Tax is relatively high, Income Tax has is broken down into "brackets" and is a pretty fair system whilst not being so complex to work out that it is expensive for the government to administer.
Income Tax has an un-taxed level of £7,475 (currently), which means that if you are part time and earn £8,000 per year you will only pay tax on £525 of your earnings, which at at 20% is £105 as well as £92.64 in NI. However if someone is earning £18,000 per year, they will be taxed at 20% for £10,525 of their earnings, giving £2,105 to the government, whilst also giving £1,292.64 in NI, and if someone is earning £28,000 per year they will pay £4,105 in Tax and £2,492.64 in NI.
The next bracket up for income tax is £42,475, anything over this point is taxed at 40%, a person earning that much will pay £7,000 in Tax and £4,229.64 in NI.
The total tax taken from each of these examples by the governments 2 income taxes are as follows.
Earn £8,000 - Total tax 2.5%
Earn £18,000 - Total tax 23.2%
Earn £28,000 - Total tax 30.8%
Earn £42,475 - Total tax 35.9%
The overall percentage of tax taken by the government goes up the more you earn, which is the way it should be, rather than going down like it does with rich people in the US (legally) or by rich-people in the UK (increasing illegally, as the government is cracking down on this immoral behavior).
I assume everyone here considers this a fair kind of tax system, and that the mega-rich should not be able to dodge taxes in the way that they are doing, and can only do because they earn enough to pay other people to avoid their taxes.