In this paper, we mainly investigate profound interconnections between combinatorial designs, linear codes, and Boolean functions. Firstly, we present a generic construction method for designs derived from Boolean functions and give a new concept of non-symmetric designs with the triple symmetric difference property (TSDP). Secondly, we provides an alternative proof for addition designs derived from plateaued functions, which need not be simple or symmetric. We characterize simple 2-designs on 2m−rpoints arising fromr-plateaued functions inmvariables, and show that addition designs from such functions with no nonzero linear structure satisfy the TSDP but not the double one, yielding non-symmetric simple 2-designs. Thirdly, we primarily explore the equivalence relationships between designs, linear codes, and plateaued functions. These investigations help resolve two open problems posed by Ding and Tang (Designs from Linear codes, Singapore: World Scientific, 2022: Problems 14.20, 14.23).We also compute the automorphism groups of addition designs ofr-plateaued functions and of the linear codes of addition designs. This work extends results by Bending (SDP designs and their automorphism groups, Ph.D. thesis, 1993), and Dempwolff and Neumann (Des. Codes Cryptogr., 57, 373–381, 2010). Finally, we yield new Boolean functions producing two families of a 2-design whose parameters coincide with those of the complement of a point-hyperplane design and a TSDP design, despite being non-isomorphic.