does the turbo assist the car itself or just hp??? as far as winning a drag race for example.?

The turbo would probably lose. Horsepower from a NA engine is going to be more readily accessible throughout the rpm range while the turbo depends on engine RPMs and the exhaust speed to maintain its boost. So when the engine is at a lower RPM the turbo is not working efficiently and the boost will be much lower.

A non-turbo engine also has a peak range, but the hp will be greater for a wider range than a turbo hp range.

usually hp in a NA engine is derived from 2 factors, displacement and RPMs. For example the Subaru WRX STI has a smaller 4 cyl turbo engine that puts out about 306 hp where as the Lexus IS 350 has a 3.5l V6 that puts out the same horse power. these are 2 horrible comparisons because one is a heavy luxury sports sedan and the other is a partially race modified light weight sedan, but if you only look at the engines, you will get the point.

I think you don't have a good understanding on what a "turbo" is?

Lets start with that... Basically it's an air pump, like a leaf blower. It pumps more air into the engine under pressure. This means you can add more fuel, and get more power from the same size engine. It's powered by the exhaust gasses as they leave the engine. This turns a little turbine, that's connected to the impeller or air pump. Hence the name "turbocharger". A supercharger is a similar device that belt driven from the engine. The are pluses and minuses to both systems, but they both boost the engines power

Now for your example with 2 "identical" cars, if one had a turbo, it wouldn't have 300 hp any more. It might make 400 hp, and should win the race.

Or they are similar cars, with different engines, making the same hp? Maybe the turbo still has the advantage because it can make 300 hp from a light 4 cyl engine, vs 300 hp from a heavy V8? Same hp, lighter car = better acceleration.

But even then it's not exact. There are things like torque curves, gear ratios, traction and turbo lag to consider, and that's going to be different for every car and engine combination.

So for example, look at the new Mustangs.

The 3.7l V6 makes 300 hp, while the 2.3 litre 4cyl makes 310 hp (because it has a turbo)

But the V6 is still marginally quicker to 60 mph, despite the 4 cyl being lighter and having more HP. Probably because the larger engine has better low end torque and no turbo lag.

The turbo car would probably lose due to turbo lag. The naturally aspirated car would have practically zero lag. Turbos are usually set up to produce high peak power. A naturally aspirated car with the same power rating can just add displacement to raise the whole powerband.