The technology of Autonomous Vehicles (AVs) and Unmanned Aerial Vehicles (UAVs) has evolved and contributed to improving road safety and traffic efficiency in Intelligent Transportation Systems (ITS). ITS applications are dependent on a communication network formed between AVs and UAVs suffer from security and privacy issues owing to vulnerable wireless communication channels. Considering these issues, SP2AP, a Physically Unclonable Function (PUF) and Elliptic Curve Cryptography (ECC)-based efficient and reliable privacy-preserving authentication protocol for secure UAV-UAV communications in IoT systems is presented in this paper. The proposed protocol not only offers anonymity and untraceability features but also mitigates UAV capture attacks. A robust informal security analysis confirms that the SP2AP protocol safeguards against various known security attacks, such as masquerade, Man-In- The-Middle (MITM), Ephemeral Secret Leakage (ESL), replay, node tampering, cloning, etc. The proposed protocol offers other security features, including mutual authentication, secure key agreement, no clock synchronization, user anonymity, untraceability, (for/back)ward secrecy, property, and drone-to-drone direct authentication. The formal security proof is performed using the Real-OR-Random (ROR) model, and the Scyther tool also demonstrates that the SP2AP protocol is more robust in terms of security and privacy. Performance analysis evaluates computation and communication costs, which show better superiority compared to similar existing protocols.