It probably depends on who you ask. Beyond the philosophical question if you're applying for food stamps those people would definetly consider living in a car being homeless. I once lived in a single-wide mobile home paying my buddy's court fines to keep him out of jail as my rent but when I told the state welfare people whose property I was living on they rubber-stamped me "homeless" without hesitation. We had even had a washer and dryer but they knew exactly the house I was living in and the property owner's name and the condition it was in so as far as they were concerned I was homeless. This was to ensure that I would get benefits. That was kind of eye-opening for me.

If Social Security is asking it's just the opposite. Homelessness to them means you have less expenses so they'll withhold part of your income because as far as they're concerned if you're homeless then you're getting free room and board. You need to give them a copy of your rental agreement just to prove you aren't getting any handouts just to collect you full benefits. When you're homeless they withhold like a third of your income which just happens to be what you'd pay for rent to the housing authority.

For me homeless is a state of mind. Home is where the heart is so if you aren't happy then your heart isn't in it which means you aren't home. If a car can be a home for you and you can be happy in your home then you're where you need to be and that to me is home but that's just philosophy.

For any practical purposes living in your car is definitely homelessness but compared to sleeping on the sidewalk you'd certainly have something to be grateful for.