This paper introduces the DISAC concept, a transformative approach for 6G wireless networks that extends the integrated sensing and communications (ISAC) concept. DISAC addresses the limitations of existing ISAC models by introducing two novel foundational functionalities: a distributed architecture and a semantic and goal-oriented framework. The distributed architecture enables large-scale and energy-efficient tracking of connected users and objects through the fusion of heterogeneous sensors. The semantic and goal-oriented framework enables the transition from classical data fusion to the composition of semantically selected information, offering new paradigms for resource optimization and multi-modal sensing performance. DISAC is built on three interrelated cornerstones: a distributed architecture that supports intelligent operations and distributed functions; a semantic and goal-oriented framework supported by machine learning and AI; and advanced high-resolution processing that leverages distributed observations. The DISAC framework combines heterogeneous and distributed sensors with a semantic-native approach to enable energy-efficient, high-resolution tracking of connected users and objects. The DISAC vision requires standardization efforts, especially concerning AI/ML-driven sensing within distributed heterogeneous architectures. It impacts various layers of the 6G ecosystem, including the physical layer, control and management planes, and the security of data and model exchanges. Achieving harmonious orchestration of radio, transport, and processing resources is of primary importance, demanding efficient and dynamic solutions. The paper details the DISAC framework, bringing together perspectives from the telecommunications industry, key verticals, and academia. It highlights the necessity of DISAC from two perspectives: use cases and standardization. Use cases such as digital twins benefit from the fusion of multi-modal sensed information and semantic type of information exchange. Standardization efforts are ongoing, with organizations like ETSI, 3GPP, and IEEE exploring the integration of AI/ML with ISAC. The DISAC vision relies on four technological enablers: a semantic framework for ISAC, an optimized and parsimonious physical layer, intelligent resource allocation, and an evolved architecture. The semantic framework enables the composition of semantically selected information and AI-based reasoning. The physical layer involves waveform optimization, channel parameter estimation, detection, and tracking. Intelligent resource allocation ensures efficient use of sensing and communication resources. The evolved architecture supports distributed processing, semantic layer interactions, and XL-MIMO and RIS-aided sensing. The DISAC vision faces challenges in theory and algorithms, proofs of concept, and standardization. These challenges require a broad view encompassing stakeholders from industry and academia, covering all aspects of the 6G value chain. The paper concludes that DISAC has the potential to increase the TRL of ISAC and unlock new possibilities for resource-efficient, accurate, and semantic network operations.This paper introduces the DISAC concept, a transformative approach for 6G wireless networks that extends the integrated sensing and communications (ISAC) concept. DISAC addresses the limitations of existing ISAC models by introducing two novel foundational functionalities: a distributed architecture and a semantic and goal-oriented framework. The distributed architecture enables large-scale and energy-efficient tracking of connected users and objects through the fusion of heterogeneous sensors. The semantic and goal-oriented framework enables the transition from classical data fusion to the composition of semantically selected information, offering new paradigms for resource optimization and multi-modal sensing performance. DISAC is built on three interrelated cornerstones: a distributed architecture that supports intelligent operations and distributed functions; a semantic and goal-oriented framework supported by machine learning and AI; and advanced high-resolution processing that leverages distributed observations. The DISAC framework combines heterogeneous and distributed sensors with a semantic-native approach to enable energy-efficient, high-resolution tracking of connected users and objects. The DISAC vision requires standardization efforts, especially concerning AI/ML-driven sensing within distributed heterogeneous architectures. It impacts various layers of the 6G ecosystem, including the physical layer, control and management planes, and the security of data and model exchanges. Achieving harmonious orchestration of radio, transport, and processing resources is of primary importance, demanding efficient and dynamic solutions. The paper details the DISAC framework, bringing together perspectives from the telecommunications industry, key verticals, and academia. It highlights the necessity of DISAC from two perspectives: use cases and standardization. Use cases such as digital twins benefit from the fusion of multi-modal sensed information and semantic type of information exchange. Standardization efforts are ongoing, with organizations like ETSI, 3GPP, and IEEE exploring the integration of AI/ML with ISAC. The DISAC vision relies on four technological enablers: a semantic framework for ISAC, an optimized and parsimonious physical layer, intelligent resource allocation, and an evolved architecture. The semantic framework enables the composition of semantically selected information and AI-based reasoning. The physical layer involves waveform optimization, channel parameter estimation, detection, and tracking. Intelligent resource allocation ensures efficient use of sensing and communication resources. The evolved architecture supports distributed processing, semantic layer interactions, and XL-MIMO and RIS-aided sensing. The DISAC vision faces challenges in theory and algorithms, proofs of concept, and standardization. These challenges require a broad view encompassing stakeholders from industry and academia, covering all aspects of the 6G value chain. The paper concludes that DISAC has the potential to increase the TRL of ISAC and unlock new possibilities for resource-efficient, accurate, and semantic network operations.