filter will remove all items from the stream that do not satisfy the condition.
takeWhile will abort the stream on the first occurrence of an item which does not satisfy the condition.
e.g.
Stream.of(1,2,3,4,5,6,7,8,9,10,9,8,7,6,5,4,3,2,1)
.filter(i -> i < 4 )
.forEach(System.out::print);
will print
123321
but
Stream.of(1,2,3,4,5,6,7,8,9,10,9,8,7,6,5,4,3,2,1)
.takeWhile(i -> i < 4 )
.forEach(System.out::print);
will print
123