Is the open loop phase response of an op amp the same as the closed loop phased response?
The closed loop response of your op-amp completely depends on the circuit you're putting your op-amp in. So, there is not 'one' closed-loop response of your op-amp.

The open-loop response describes the response from the op-amp inputs to its outputs. This is a useful measure, because this is completely independent of the other components in your circuit - you're only measuring the op-amp itself.

I come from a mechanical engineering background, so op-amps aren't my area of expertise, but consider a ideal op-amp in buffer configuration (gain from input to output: 1) or a simple inverting amplifier (gain from input to output: -R2/R1). So here, the closed loop responses are completely different even though we have an ideal op-amp! So, it all depends on how exactly we 'close the loop'.

If you're unsure how to calculate the closed-loop response yourself, I think that's best asked in another question. I'll give one hint: in typical system block diagrams, the 'transfer function' of a block is exactly the open loop response of that block.