there is no difference. both of them mean "they're playing."

Similar, with little difference. If you are asking that what they(the kids) are doing, you can answer '孩子们在玩儿呢。/孩子们玩着呢。'. In fact, I prefer the former one. I seldom answer with the latter one. If you ask your children to go and play, you can answer '孩子们玩着呢。' 这句话表示 ‘孩子们已经在玩了，你不用去叫了。’ **Welcome any comment.

If you are at beginner or intermediate level of Chinese, no need to figure out the difference. You can consider them as two ways to express the same thing. If you are an advanced learner and you live in China, when you hear people say 孩子们玩儿着呢, maybe they imply that don't disturb the kids. Just my opinion~

孩子们在玩儿呢。& 孩子们玩儿着呢。 They mean exactly the same thing, which is" This kids are playing now." In the first sentence, there is a word "在", it is a short form of "正在", which means now, currently, at this very moment. In the second sentence, there is a word "着", this is a little trickier than the former one, it often means that the action is ongoing at the moment. For more details about these two words, you could refer to links below(they are in Chinese though): 在：http://baike.baidu.com/link?url=11YT8gkv60kfm7374CnVJbSDuT9QCwJjF-Lc_ocbowj77bbDktvy1JNy6sucNG7ejDepIth1iReB5cawk2TRE_ 着：http://baike.baidu.com/item/%E7%9D%80/4344756 Hopes the above could be helpful to U.

you gave me advice - I recommend you to stop sending messages if person really wanna communicate with you, he will write you, he don't wanna anymore, he won't. you know i will miss... you told - I should check whether or not he has the willingness to have contact. you must be patient for checking this... but i love my friends, crazy missing.... i told you before - i have only 2 friends. how to be sillent? how to be patient when i am loosing them. you really burned all my heart and left me alone, when i so need to be close and so ask to be with me. So difficult to find real friend in the internet.... So hard to find even in real life ... so easy to loose friend in the internet, just delete from contact list .... but you both - were real friends for me... how to delete from heart? I forgave you. forgive me...