What is the difference between "in the playground" and "on the playground"

Solution 1:

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.

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: among the general public, as in

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

Solution 2:

Whether to use in or on is a matter of Dimensionality.

Since playground can be thought of

• either as a 2-dimensional bounded ground surface (hence requiring on),
• or as a 3-dimensional outdoor space (hence requiring in),

both on the playground and in the playground are correct and both are common.

Their metaphor themes are coherent --
i.e, if one is on the bounded 2-D play ground, then one is also in the 3-D space it defines,
and vice versa.