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We argue that recently proposed by Amelino-Camelia et all [1,2] so-calleddoubly special relativity (DSR), with deformed boost transformations identicalwith the formulae for $\kappa$-deformed kinematics in bicrossproduct basis is aclassical special relativity in nonlinear disguise. The choice of symmetriccomposition law for deformed fourmomenta as advocated in [1, 2] implies thatDSR is obtained by considering nonlinear fourmomenta basis of classicalPoincar\'{e} algebra and it does not lead to noncommutative space-time. We alsoshow how to construct large two classes of doubly special relativity theories -generalizing the choice in [1,2] and the one presented by Magueijo and Smolin[3]. The older version of deformed relativistic kinematics, differingessentially from classical theory in the coalgebra sector and leading tononcommutative $\kappa$-deformed Minkowski space is provided by quantum$\kappa$-deformation of Poincar\'e symmetries.Comment: LaTex, 15 pages; minor corrections of formulae (1) and (4), footnote  2 added. Journal references adde

DOUBLY SPECIAL RELATIVITY VERSUS κ-DEFORMATION OF RELATIVISTIC KINEMATICS