The other kind is your inclusion of other tools as subsidization. Enough said, you're boring me.
What you cannot overcome is the economic effect of those "other tools" is (or can be, depending on terms) identical in every way to that of a cash grant. So all you have left is pedantry...
You'll ignore the following, but it's not for you.....
The problem from my perspective is the false distinction between a "subsidy" versus a "Tax incentive" is how we end up with a "loophole" ridden tax code full of hidden subsidies, that never show up in the annual budgets, that don't require votes of Congress to appropriate annually, and total about $1.5 trillion a year in foregone revenue, which is not quite but approaching total income tax collections per year.
The $200 billion/year in "incentives" for employer provided health insurance are a good example. People don't know or care about the total cost of their employer provided policy because it's tax free to them (they care about their share...), and fully deductible by the employer. That arrangement lowers the cost of providing health insurance to employees, and therefore directly subsidizes providing health insurance as compensation versus cash salary, is a good thing - the subsidies WORK, the vast majority of employers provide health insurance and the subsidies help. But people don't see this huge subsidy and so don't even know they benefit.
So they can oppose the direct ACA subsidies of the poor,
and support the subsidies of their own health insurance cumulatively totaling $200 billion per year, and never even confront the disconnect. If we cut all employees a check for the tax savings, versus them just not seeing the value of the compensation they get in the form of very valuable insurance in their W-2, we'd all understand the issue better. But it's even worse when we pretend that the tax savings from tax free employer provided insurance are fundamentally different than a cash grant. That's the fundamental lie in the false distinction you're trying to draw.
The tax deduction for state and local taxes is another example. The deduction allowed states and cities to shift the cost of their taxes, a form of tax exporting, onto federal taxpayers through deductions, it lowered the after tax cost of those taxes for those able to itemize. So it was a subsidy of the SALT burden by federal taxpayers. Someone in the top bracket only 'paid' 65% of their total SALT burden due to the federal tax deduction at the 35% marginal rate. We federal taxpayers paid the rest as a group. We need to be honest about that - it WAS a federal subsidy of SALT. Good or bad thing is up for debate, but we can't debate it honestly without calling it what is IS.
If Congress just cut a check to NYC residents every year in an amount equal to the tax savings, we all KNOW the discussion would be entirely different. We'd see wealthy NYC residents getting six and maybe seven figure checks from the feds while some farmer in Iowa isn't getting a penny cause he doesn't itemize. But the economic impact at the top level is identical. Foregone federal revenue from the deduction is functionally identical to that alternative cash grant to the taxpayers, for the feds and the taxpayers.