We present measurements of two-particle differential number correlation functions R2 and transverse momentum correlation functions P2, obtained from p-Pb collisions at 5.02 TeV and Pb-Pb collisions at 2.76 TeV. The results are obtained by using charged particles in the pseudorapidity range |η|<1.0 and transverse momentum range 0.2<pT<2.0 GeV/c as a function of pair separation in pseudorapidity, |Δη|, azimuthal angle Δφ, and for several charged-particle multiplicity classes. Measurements are carried out for like-sign and unlike-sign charged-particle pairs separately and combined to obtain charge-independent and charge-dependent correlation functions. We study the evolution of the width of the near-side peak of these correlation functions with collision centrality. Additionally, we study Fourier decompositions of the correlators in Δφ as a function of pair separation |Δη|. Significant differences in the dependence of their harmonic coefficients on multiplicity classes are found. These differences can be exploited, in theoretical models, to obtain further insight into charged-particle production and transport in heavy-ion collisions. Moreover, an upper limit of nonflow contributions to flow coefficients vn measured in Pb-Pb collisions based on the relative strength of Fourier coefficients measured in p-Pb interactions is estimated.