I think the question in the title and the question in the body are quite different. As far as *playground* is concerned, [both *in* or *on* are fine][1].

*In the ground*, as Sirish points out, has the literal meaning of being *in* the ground, as in:

> There are lots of minerals in the ground.

> He found a beautiful stone in the ground.

*On the ground* has two meanings. One is the literal meaning of being on the surface of the ground, as in:

> There's a big rock on the ground.

*On the ground has* also [an idiomatic meaning][2]: *among the general public*, as in

> Their political ideas have a lot of support on the ground.


  [1]: https://books.google.com/ngrams/graph?content=in%20the%20playground%2C%20on%20the%20playground&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cin%20the%20playground%3B%2Cc0%3B.t1%3B%2Con%20the%20playground%3B%2Cc0
  [2]: http://dictionary.cambridge.org/dictionary/british/on-the-ground