A BehaviorSubject holds one value. When it is subscribed it emits the value immediately. A Subject doesn't hold a value.

Subject example (with RxJS 5 API):

const subject = new Rx.Subject();
subject.next(1);
subject.subscribe(x => console.log(x));

Console output will be empty

BehaviorSubject example:

const subject = new Rx.BehaviorSubject(0);
subject.next(1);
subject.subscribe(x => console.log(x));

Console output: 1

In addition:

• BehaviorSubject should be created with an initial value: new Rx.BehaviorSubject(1)
• Consider ReplaySubject if you want the subject to get previously publised values.

BehaviourSubject

BehaviourSubject will return the initial value or the current value on Subscription

var bSubject= new Rx.BehaviorSubject(0);  // 0 is the initial value

bSubject.subscribe({
  next: (v) => console.log('observerA: ' + v)  // output initial value, then new values on `next` triggers
});

bSubject.next(1);  // output new value 1 for 'observer A'
bSubject.next(2);  // output new value 2 for 'observer A', current value 2 for 'Observer B' on subscription

bSubject.subscribe({
  next: (v) => console.log('observerB: ' + v)  // output current value 2, then new values on `next` triggers
});

bSubject.next(3);

With output:

observerA: 0
observerA: 1
observerA: 2
observerB: 2
observerA: 3
observerB: 3

Subject

Subject does not return the current value on Subscription. It triggers only on .next(value) call and return/output the value

var subject = new Rx.Subject();

subject.next(1); //Subjects will not output this value

subject.subscribe({
  next: (v) => console.log('observerA: ' + v)
});
subject.subscribe({
  next: (v) => console.log('observerB: ' + v)
});

subject.next(2);
subject.next(3);

With the following output on the console:

observerA: 2
observerB: 2
observerA: 3
observerB: 3

I just created a project which explain what is the difference between all subjects:
https://github.com/piecioshka/rxjs-subject-vs-behavior-vs-replay-vs-async