Condition.await and LockSupport.park differences

Question

What are the differences between
java.util.concurrent.locks.LockSupport.park()
and
java.util.concurrent.locks.Condition.await()?
From the API it seems they have the same behaviour:
"Disables the current thread for thread scheduling purposes unless the permit is available..." for the first,
"Causes the current thread to wait until it is signalled or interrupted..." for the second.
Are they equals? If no, what are the differences? Can they be used together, for example:
class MyClass {
     Lock lock;
        Condition condition;
        Handler handler;
         //constructor
         MyClass() {
               // initializes and then starts handler
        public void method1() {
                // do something...
                LockSupport.unpark(handler);
                condition.signal();
        private class Handler extends Thread {
          public void run(){
                        while (true) {
                    while(! something) {
                         try {
                              LockSupport.park();
                              condition.await();
                              // do something
                         } catch (InterruptedException e) {
}

Answer 1

Many of classed and interfaces in the java.util.concurrent package are used as building blocks for
higher level concurrency supporting classes. In particular, Condition object is associated with
Lock object and a single Lock can have multiple Conditions hereby enabling single Lock object
having multiple wait sets(await/unlock pairs). LockSupport class only provides one single such
pair through its simple static methods.