63Cu NQR spin-lattice and spin-spin relaxation measurements are used to compare the effects of charge doping (such as in La2-y Sry CuO4) with the ones due to the spin vacancies induced by the Zn2+S = 0 for Cu2+S = 1/2 substitution in La2CuO4. In particular the possible role of itinerant and/or localized singlets in driving this typical quantum Heisenberg 2D antiferromagnet in the quantum disordered regime is addressed. The in-plane magnetic correlation length ξ2D in the paramagnetic phase is quantitatively extracted and its dependence on charge and spin doping is derived. It is found that ξ2D(x, T) in La2Cu1_xZnxO4, as well as the drop in the Neel temperature TN(x), can consistently be explained by taking into account the effect of the spin vacancies on the spin stiffness ϱs (x), in the framework of a conventional dilution-like model. When the singlets are itinerant (as in La2-y SryCuO4) ξ2D(y,T) and correspondingly ϱs(y) are markedly more affected. Furthermore the dramatic drop in TN(y) cannot longer be explained by a conventional mean field description for the interplane coupling.