There are two approaches to the construction of formal groups. The functional lemma proved by Hazewinkel allows to make formal groups with coefficients from a ring of zero characteristic by means of the functional equations using a certain ideal of this ring, overfield and a ring homomorphism with certain properties (for example, identical, and for a local field the Frobenius homomorphism can be chosen). There is a convenient criterion for the isomorphism of formal groups constructed by Hazewinkel’s formula, as well as a formula for logarithms (in particular, the Artin-Hasse logarithm). At the same time, Lubin and Tate construct formal groups over local fields using isogeny, and Honda construct formal groups over discrete normalized ring of characteristic fields, introduces a certain noncommutative ring induced by the original ring and a fixed homomorphism. The paper establishes a connection between the classical classification of formal groups (standard, generalized and relative formal Lubin-Tate groups and