Is Periodic Convolution Same as Circular Convolution?
You did not give specific details on how you define periodic or circular. Assuming standard definitions, the answer is yes.

Standard infinite-support data is treated with standard convolution. When the support  is finite, the "outer unknown samples" require assumptions. 

Zero-valued outside samples is a common assertion. Another option, often used with Fourier or wavelet transforms, consists in arranging finite-support data on a ring or torus, the first sample following the last one. 

It is often termed periodic, cyclic or circular, with a similar meaning.