What is the diff between the Media transfer protocal and Picture Transfer Protocol
MTP is the better option in most cases, since the protocol is actually designed for this use.

PTP is offered as an alternative since Macs don't understand MTP by default (you need to install "Android File Transfer" on the Mac to make MTP work). This protocol was designed for PCs to access photos from digital cameras, so it can only access the photos on the phone, and it might trigger a photo management app on the PC instead of a file manager.

To learn more about why MTP was introduced, see my answer to Why is Android File Transfer necessary?