The Industrial Internet of Things (IIoT) integrates cyber-physical systems, edge-cloud computing, Artificial Intelligence (AI), and advanced connectivity to enable intelligent, data-driven operations across manufacturing, energy, transportation, and healthcare. The convergence of Operational Technology (OT) and Information Technology (IT), together with pervasive AI-driven automation, complicates meeting the joint requirements of performance, adaptability, and security (PAS). This survey adopts an explicitly AI-centric view of PAS and reviews IIoT research spanning deep reinforcement learning (DRL), multi-agent reinforcement learning (MARL), digital twins (DTs), federated and collaborative learning, graph neural networks (GNNs), blockchain-assisted analytics, and lightweight and post-quantum cryptography. The reviewed approaches are analyzed across device, edge, fog, cloud, and application layers under industrial constraints such as latency, reliability, resource limits, safety requirements, and regulatory compliance. A PAS-centric taxonomy is introduced that links technique families to deployment layers and application domains, and recurring trade-offs among PAS dimensions are summarized. Open challenges are identified in multi-objective optimization, semantic interoperability, lifecycle validation, and governance, with directions outlined toward secure and sustainable Industry 5.0 IIoT ecosystems.