Authors’ abstract: In this paper, the two methods for finding rational general solutions of first-order algebraic ODEs introduced by L. X. C. Ngô and F. Winkler see e.g. [Publ. Math. 79, No. 3–4, 573–587 (2011; Zbl 1249.34006)] and N. T. Vo et al. [J. Symb. Comput. 87, 127–139 (2018; Zbl 1390.34007)] are compared. Both methods assign some affine algebraic set to an algebraic ODE. Provided the assigned algebraic sets are suitably parametrizable, the initial ODE can be reduced to a more fundamental (set of) differential equation(s). The two approaches lead to a common rational parametrization in certain situations, in which case the corresponding derived differential equation(s) are shown to coincide. Finally, a discussion on relations between certain classes of first-order algebraic ODEs with respect to their rational general solvability is provided.