Hello Moeedeng
Both PPP and HDLC are Data-link layer protocols that were originally used to connect devices in a point-to-point manner over a serial connection. HDLC is a Cisco Proprietary protocol while PPP is an open standard originally defined in RFC 1661. HDLC is supported only by Cisco devices, while PPP is generally supported by all vendors. PPP includes features such as authentication while HDLC does not.
Overall, PPP is much more widely used, and has been adapted and developed to be used in PPPoE and PPPoA derivatives, primarily for authentication in xDSL implementations. It is also often used over other links including specialized radio links and fiber optics. HDLC has limited use and only within Cisco equipment.
You can see the differences in implementation at the following lessons:
I hope this has been helpful!
Laz