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We derive the non-relativistic $c\to\infty$ and ultra-relativistic $c\to 0$limits of the $\kappa$-deformed symmetries and corresponding spacetime in (3+1)dimensions, with and without a cosmological constant. We apply the theory ofLie bialgebra contractions to the Poisson version of the $\kappa$-(A)dS quantumalgebra, and quantize the resulting contracted Poisson-Hopf algebras, thusgiving rise to the $\kappa$-deformation of the Newtonian (Newton-Hooke andGalilei) and Carrollian (Para-Poincar\'e, Para-Euclidean and Carroll) quantumsymmetries, including their deformed quadratic Casimir operators. Thecorresponding $\kappa$-Newtonian and $\kappa$-Carrollian noncommutativespacetimes are also obtained as the non-relativistic and ultra-relativisticlimits of the $\kappa$-(A)dS noncommutative spacetime. These constructionsallow us to analyze the non-trivial interplay between the quantum deformationparameter $\kappa$, the curvature parameter $\eta$ and the speed of lightparameter $c$.

The $\kappa$-Newtonian and $\kappa$-Carrollian algebras and their noncommutative spacetimes