I'm sorry, but I just can't agree with you. If we start to take words and stretch their meaning beyond the agreed upon definition then any argument becomes meaningless. 'subsidy' is a very clearly defined term.
"a sum of money granted by the state or a public body to help an industry or business keep the price of a commodity or service low."
If the state is issuing a tax on something it is by definition not subsidized.
I hate quoting wikipedia, but the definition they use is far wider:
"A subsidy is a form of financial aid or support extended to an economic sector (or institution, business, or individual) generally with the aim of promoting economic and social policy.[1] Although commonly extended from government, the term subsidy can relate to any type of support – for example from NGOs or as implicit subsidies. Subsidies come in various forms including: direct (cash grants, interest-free loans) and indirect (tax breaks, insurance, low-interest loans, accelerated depreciation, rent rebates)."
That would at least indicate that the definition is by far not as clear as you would like to have it.
Diesel is taxed lower with the aim of promoting two economic goals: lowering total CO2 output and supporting the transportation sector. It falls really right under that definition.
But it's not a tax break. You pay more taxes on diesel than on other things, except gas. Are all other things subsidized because they don't have the gas tax?
It’s the same thing as gas: fuel, to power a car. It just happens to be a slightly different mix of hydrocarbons. It’s sold from the same machine, at the same place for the same purpose. And it’s taxed the same way in pretty much all European countries, Germany is the odd outlier. Different kinds of petrol are taxed the same way, too.
The same mix of hydrocarbons that is diesel fuel is sold for heatings as well (Heizöl) It’s taxed different - since it’s a different use. And since that one is taxed much lower, they add a red color and using it as fuel is tax evasion and lands you in jail.
The Energiesteuergesetz is the law which regulates the taxes. It has individual tax rates for Benzin (gasoline), Diesel, CNG (gas), LPG (autogas), heavy oil.
Per fixed amount of energy, diesel is the second highest taxed energy carrier.
"a sum of money granted by the state or a public body to help an industry or business keep the price of a commodity or service low."
If the state is issuing a tax on something it is by definition not subsidized.