What are Complication and Simplification in Chess? I want to know whether I understood these concepts correctly.

Complication:
I think, in a given position, usually the side that is slightly inferior tries to make moves that somehow put considerable strain on the better side about which action to choose. Thus it tests one's ability to clearly calculate the labyrinth of all possible variations. Generally the lesser mortal fails and hence passes on the edge to the side that created such complication. 

Simplification:
I presume simplification is the reverse of it. By simplification I mean reducing number of pieces while maintaining the winning edge. I suspect the general idea behind simplification is to prevent any counter-play by the opponent. I guess the side with winning advantage always tries to simplify matters while the other side indulges in complicating.

Is it correct?
I don't think its easy to answer your question since both of these concepts can have multiple definitions depending on who you ask, but I'll give it a shot.

Generally, in the case where one side is winning, your conceptual understanding is correct. 

When the position is equal, creating complications or simplifications are a matter of player preference.  For example, if Player A is rated lower than Player B, then Player A may be more apt to trade down (simplification) in order to get a drawish position.  In that case it is assumed that Player A would be content with a draw. Thus, reinforcing the statement that complications and simplifications are a matter of player preference.