What is the difference between .stream() and Stream.of?

The second one does not do what you think it does! It does not give you a stream with the elements of the collection; instead, it will give you a stream with a single element, which is the collection itself (not its elements).

If you need to have a stream containing the elements of the collection, then you must use entities.stream().

We can take a look at the source code:

/**
 * Returns a sequential {@code Stream} containing a single element.
 *
 * @param t the single element
 * @param <T> the type of stream elements
 * @return a singleton sequential stream
 */
public static<T> Stream<T> of(T t) {
    return StreamSupport.stream(new Streams.StreamBuilderImpl<>(t), false);
}

/**
 * Returns a sequential ordered stream whose elements are the specified values.
 *
 * @param <T> the type of stream elements
 * @param values the elements of the new stream
 * @return the new stream
 */
@SafeVarargs
@SuppressWarnings("varargs") // Creating a stream from an array is safe
public static<T> Stream<T> of(T... values) {
    return Arrays.stream(values);
}

As for Stream.of(), when the input variable is an array, it will call the second function, and return a stream containing the elements of the array. When the input variable is a list, it will call the first function, and your input collection will be treated as a single element, not a collection.

So the right usage is :

List<Integer> list = Arrays.asList(3,4,5,7,8,9);
List<Integer> listRight = list.stream().map(i -> i*i).collect(Collectors.toList());

Integer[] integer = list.toArray(new Integer[0]);

List<Integer> listRightToo = Stream.of(integer).map(i ->i*i).collect(Collectors.toList());

I myself keep getting confused about this so I might as well leave this here for future reference:

import java.util.stream.IntStream;
import java.util.stream.Stream;

import static java.util.Arrays.*;
import static java.util.stream.Stream.*;

class Foo {
    void foo() {
        Stream<Foo> foo; 

        foo =     of(new Foo(), new Foo());
     // foo = stream(new Foo(), new Foo()); not possible

        foo =     of(new Foo[]{new Foo(), new Foo()});
        foo = stream(new Foo[]{new Foo(), new Foo()});

        Stream<Integer> integerStream; 

        integerStream =     of(1, 2);
     // integerStream = stream(1, 2); not possible

        integerStream =     of(new Integer[]{1, 2});
        integerStream = stream(new Integer[]{1, 2});

        Stream<int[]> intArrayStream =     of(new int[]{1, 2}); // count = 1!
        IntStream intStream          = stream(new int[]{1, 2}); // count = 2!
    }
}

1)

Stream<String> stream1 = entities.stream()

2)

Stream<Collection<String>> stream2 = Stream.of(entities)

So use 1, or for 2

Stream<String> stream3 = Stream.of("String1", "String2")