I agree with this. As "Stoit" means standing, the car is standing on the street, it is therefore parked. If we say the car is on the street, it is probably moving, or at least, it is in the lane of traffic. I had further thoughts about this, though. If someone asked, "Is your car in the parking lot?" I might answer, "No, it's on the street." And perhaps the Russian sentence could imply that the car is waiting on the street (like a taxi) and not necessarily parked.
No, if we say, машина стоит, we mean the car/truck is parked. And на улице means outdoors/outside, not necessarily "on thre street". We can also say Moя машина стоит на улице when speaking of a washing machine while we are moving house, for example. If a car is moving on the street, we will say "машина едет по улице, and if it is standing in a lane of traffic, we will say "машина стоит в пробке / на светофоре". If a car with the driver is waiting outside, then the verb will be "ждёт" because "стоит на улице" implies that there is no driver in it.
If a car is stopped in a traffic jam, the Russian expression is «машина стоит в пробке» or, if you are in the car, «я стою / мы стоим в пробке». «На улице» simply means “outdoors” unless the name of the street follows. If a car has just pulled over, we are more likely to use the verb «остановилась», especially if the driver is still in it, and «на улице» is never used n that case.
In Canada and perhaps the eastern US as well, NO STANDING is a common road sign. It refers to a car that is effectively parked but one where the driver is seated and could move the car if required. Probably it originated from an argument. "The sign says No Parking. I'm not parked, I'm just standing or waiting."
In Russian, it's different. We have a special sign equivalent to NO STANDING called "Остановка запрещена" not to be confused with "Стоянка запрещена" = NO PARKING. If we want to tell somebody they cannot park in a certain place, we will say, "В этом месте нельзя стоять/парковаться". The word парковаться didn't come into use until early 1990s. For "no standing" we will say "здесь нельзя останавливаться / стоять дольше пяти минут".
Refer to Dmitry_Arch response to my earlier post. Probably, it is ok to say "My car is parked outside." I'm not sure of the shades of meaning compared to Russian, because if we say that in English, it doesn't usually just mean the car is out-of-doors or not in the garage, it more likely means the car is in front of the house or door, i.e. close by. It may or may not be on the street (could be in the driveway).