Is there any difference between two?

[MahaB82A]

Offset Path & Outline Stroke  comes under Effect & Object. Is there any difference?

[Monika Gause]

They are more different than they are similar. 

Outline stroke outlines strokes (without actually outlining anything, it just pretends, because it is an effect)

Offset path enlarges or shrinks shapes. Only when applied to an open path it might look like it does the same as outline stroke (but only when you offset with 0). 

[MahaB82A]

What I want to know is same name [Offset Path & Outline Stroke] comes under different drop down menu [Effect & Object]. Are Both similar or not. 

[Doug A Roberts]

The commands under the object menu will alter existing paths or create new ones respectively. The effects replicate them but as live effects that can be applied non-destructively to objects and individually to separate fills and strokes.

[Jacob Bugge]

Maha,

In addition to what Monika and Doug said, there are differences in both respects.

The Object way makes actual changes to the original path, and in this connexion Offset Path creates a new path while keeping the original one, so you have two paths, the new one offset from the original one.

The Effect way is about appearance with no change of the original path, and the appearance is the same as with the Object way for Outline Stroke, whereas the appearance is different for Offset Path because only the offset path appears while the original path becomes invisible.

The Effect way can be Expanded to give actual changes like the Object way, but differently for Offset Path and Outline Stroke:

For Outline Stroke, Expanding the Effect gives the same as the Object way: a path changed from Stroke to Fill.

For Offset Path, Expanding the Effect creates a new path corresponding to the appearance of only the offset path whereas the invisible original path disappears, so you have only one path: the offset one.