The best way to understand this is to print copies of your federal and state returns and read them. Even though the tax code that determines what counts as income or a deduction can be complicated, the tax form itself is a simple addition and subtraction problem (this income plus that income minus that deduction).
Federally, your adjusted gross income is all your income added up, minus certain "above the line" deductions (like deductible IRA and HSA contributions, teacher expenses, and a few other special items.) Then you subtract your personal deductions and itemized or standard deductions, plus a few other special deductions, to get your taxable income.
So your taxable income is always less than your adjusted gross income.
Your federal and state adjusted gross income and taxable income may be different. Some federal deductions may not be allowed by the state, and the state may have some deductions not allowed by the IRS. Grab a beer or a cup of coffee and read your forms, it's not that scary.
