I'm a newbie to Java programming, trying to get the hang of OOP.
Just my 2 cents — I will try to make it short as many interesting things have already been said. But, in fact, there is two questions here. One about "OOP" and one about how it is implemented in Java.
First of all, yes, you have a car in your garage. So your assumptions are right. But, Java is a statically typed language. And the type system in the compiler can only "know" the type of your various object by their corresponding declaration. Not by their usage. If you have an array of Vehicle, the compiler only knows that. So it will check that you only perform operation allowed on any Vehicle. (In other words, methods and attributes visible in the Vehicle declaration).
You can explain to the compiler that "you in fact know this Vehicle is a Car", by using an explicit cast (Car). the compiler will believe you -- even if in Java there is a check at run-time, that might lead to a ClassCastException that prevent further damages if you lied (other language like C++ won't check at run-time - you have to know what you do)
Finally, if you really need, you might rely of run-time type identification (i.e.: instanceof) to check the "real" type of an object before attempting to cast it. But this is mostly considered as a bad practice in Java.
As I said, this is the Java way of implementing OOP. There is whole different class family of languages broadly known as "dynamic languages", that only check at run-time if an operation is allowed on an object or not. With those languages, you don't need to "move up" all the common methods to some (possibly abstract) base class to satisfy the type system. This is called duck typing.
