Apologies if this is obvious and I'm just being dense, but how do you count your *mortgage* for purposes of figuring out your FIRE budget?

I have about $200k left on my mortgage, and my monthly payments are roughly the same as they would be if I were renting. Assuming I have $1 million invested (not my real number), then as a renter without a mortgage, the 4% rule gives me $40k/year, but as a homeowner, subtracting my mortgage (without adding the equity value) gives me a NW of $800k, and the 4% rule then gives me only $32k/year. Under both scenarios, my income producing assets and my monthly expenses are (roughly) the same. Do I plan for a retirement of $40k/year, or $32k/year?

The way I do it is to omit the mortgage (P+I) from my expenses / nest egg calculations, and then add the sum of the leftover mortgage (when you RE) back in. Your investment return should be higher than your mortgage rate, so the nest egg portion that equals the mortgage remaining (at the point of retirement) should be enough to pay your mortgage payment (though you could also opt to just pay it off exactly at that point.) Your taxes/insurance will stick around whether you have a mortgage or not, so you should include them in expenses.

In your example, while you

*have* $1 million invested in both cases, your net worth (excluding equity) is $200k lower in the example with a mortgage. And as long as are living in the house, the equity isn't useful for paying bills. Of course, depending on where you live, your expenses with rent would be higher or lower than what they'd be with a mortgage, so it's not directly comparable.

In your example, assuming you keep the house/mortgage, you plan for a retirement of $32k/year (not including mortgage P+I).

ETA: I think the confusion in your example is "expenses are roughly the same" - but one of those includes rent while the other includes mortgage. Let's just say both your rent and your mortgage are $8k/year. Now you have $32k/year left for all the rest of your expenses, whether you rent or own.