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

In the ground (inside), on the ground (top),.I use on the ground only. For instance, "Treasure is in the ground",..where as "Something dropped on the ground beside her".

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.

In this case, the line between in and on is a little blurry, and both terms could be used correctly.

However, if we had to make a distinction, we could probably say that

He is playing in the playground

...means that he is inside a defined area, set aside for play, referred to as the playground, possibly with the implication that this playground is a standalone area. It would normally be used when the speaker is outside the playground.

He is playing on the playground

...is a more context-sensitive. It could mean:

• That 'he' is on the designated playground area attached to a school or other facility

• That the play area is divided into a grass area and a paved or padded area, and 'he' is playing on the prepared area

• That there is a climbing set or other play equipment set up in the play area, and he is playing on that equipment (commonly colloquially called a playground).

This would also more often be used if the speaker is inside the area being referred to, to specify a more precise location within the school/play area.

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.

Both in and on the playground is fine because playground has an entry gate so we can use both in or on. But if it is in ground then it will be wrong.