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Digital twin networks (DTNs) serve as an emerging facilitator in the industrial networking sector, enabling the management of new classes of services, which require tailored support for improved resource utilization, low latencies and accurate data fidelity. In this paper, we explore the intersection between theoretical recommendations and practical implications of applying DTNs to industrial networked environments, sharing empirical findings and lessons learned from our ongoing work. To this end, we first provide experimental examples from selected aspects of data representations and fidelity, mixed-criticality workload support, and application-driven services. Then, we introduce an architectural framework for DTNs, exposing a more practical extension of existing standards; notably the ITU-T Y.3090 (2022) recommendation. Specifically, we explore and discuss the dual nature of DTNs, meant as a digital twin of the network and a network of digital twins, allowing the co-existence of both paradigms., Comment: Funding: (i) European Union under the Italian National Recovery and Resilience Plan (NRRP) of NextGenerationEU, partnership on "Telecommunications of the Future" PE00000001 - program "RESTART", (ii) RA Science Committee grant No. 22rl-052