A detailed comparison between the magnetic behaviours of the 'as-prepared' ap-Ni(x)Al(100-x) alloys with x = 74.3, 74.8, 75.1 and 76.1 at.% (that have both compositional disorder and site disorder) and 'annealed' counterparts (that have only compositional disorder) over a wide range of temperatures and magnetic fields (H) permits us to draw the following conclusions about the role of disorder. Regardless of the type of disorder, Curie temperature, T(C), and spontaneous magnetization at 0 K, M(0), decrease in accordance with the power laws T(C)(x) = t(x)(x -x(c))(tau) and M(0)(x) = m(x) (x -x(c))(psi) as x -> x(c) (the threshold Ni concentration below which the long-range ferromagnetic order ceases to exist). Site disorder lowers the value of x(c) by nearly 1 at.% Ni, enhances T(C) for a given composition (more so as x -> x(c)) by increasing the number of Ni nearest neighbours for a given Ni atom, and leaves M(0) essentially unaltered because site disorder has essentially no effect on the density of states, N(E(F)), at the Fermi level, E(F), and the shape of the density-of-states curve near E(F) (except for x approximate to x(c), where site disorder tends to primarily enhance N(E(F)) and thereby stabilize long-range ferromagnetic order for Ni concentrations below the threshold concentration, x(c) congruent to 74.6 at.%, dictated by compositional disorder). At low and intermediate temperatures, spontaneous magnetization, M(T, H = 0), as well as the 'in-field' magnetization, M(T, H), exhibit non-Fermi liquid behaviour in the samples ap-Ni(74.3) and ap-Ni(74.8). As x(c) is approached from above, i.e. as the compositional disorder increases, stronger deviations from the Fermi liquid behaviour occur and the temperature range over which the non-Fermi liquid behaviour persists widens. In contrast, the ap-Ni(75.1) and ap-Ni(76.1) alloys follow the behaviour that the self-consistent spin-fluctuation theory predicts for a weak itinerant-electron ferromagnet with no disorder. Both compositional disorder and site disorder have no effect on the critical behaviour of the alloys near the ferromagnetic-to-paramagnetic phase transition.