Cry for x Cry over: Qual a diferença

Hello everybody,

I came across with two expressions that involve the verb cry. I saw them in two different songs.

The first is cry over: Why should I cry overyou? ( No meu entendimento seria Por que eu deveria chorar por você?)

The other is cry for: Don't cry forme! (Não chore por mim!)

The question is: Cry over and cry for have the same meaning or are there diferences?

I look forward to your responses!

So long