You’re right, when people talk about fossil fuel subsidies, that’s thinking of government gifts and tax breaks. My point is that this is a deeply inadequate way to think about it. If you only look at these, and compare fossil fuels to renewables, you’ll come away thinking that fossil fuels are far cheaper than they actually are.
In the case of this discussion, you're looking at it backwards. The subject of fossil fuel subsidies was brought up in comparison to subsidies for renewables which in this case were already defined as specific government programs. If it weren't for that, I wouldn't be being such a stickler. However given that we are comparing renewables to fossil fuels we need to be sure that we are measuring the same thing and to include externalities when measuring fossil fuels and not when measuring renewables is to be not measuring the same thing. (I actually got confused when I first saw the IMF link so I know my concern isn't hypothetical.)
Yes, I get that the case can be made that cost of using fossil fuels is more that the sum of direct gifts by the government to fossil fuel companies (fucking duh!) but that can be expressed without implying that governments gave $5.2T in tax dollars directly to fossil fuel companies in 2017. Where confusion is possible, it's best to make distinctions and clarify what is meant.
We can measure direct subsidies by measuring real and effective tax rates.
We can measure indirect subsidies like healthcare costs paid by Medicare with subjective valuations of human life and rough estimates of the value of a person's health and contribution to growth in GDP, and future economic security.
But who has the time for this when we're busy paying to help folks who require disaster relief services from the government and NGOs (neither of which are preventing further escalations in costs)
Define the terms however you like, as long as you are careful to not to induce people to believe someone that is untrue.
If you compare fossil fuels and renewables based on the number of letters in their names, that’s the same thing for both, but it’s not useful.
Comparing explicit monetary subsidies is like that. If you want to include the implicit ones for renewables as well, you definitely should. But giving up and only comparing direct monetary subsidies gives you a woefully incomplete and misleading picture.
There's another reason this is important and it is with regard to the big picture. A lot of people already know what subsidy means and understand it to mean direct government gifts. When you use a different definition of a commonly understood word, what you are doing is defining it stipulatively. If you don't clarify that you are using a stipulative definition ahead of time, then you are committing a fallacy of equivocation. It doesn't matter if you think that your stipulative definition makes more sense or is more useful, people have to be using words the same way in order to communicate. I'd rather not give climate denialists any more fuel than is absolutely necessary and confusing equivocations are unnecessary. Talking about subsidies when you mean subsidy and talking about costs when you mean cost helps avoid them.