The relative phase of nonlinear waves is a crucial parameter in establishing their structure, properties, and types, as wellas in nonlinear wave interactions. In this paper, we construct the solution of the Kuznetsov-Ma breather, soliton, and the interactionbetween soliton and breather with relative phase on the plane-wave background of the Hirota model. Exploring the relative phaseinduced conversion of Kuznetsov-Ma breather into different solitons, and the relative phase induced soliton state transition duringa breather-soliton collision.First, the study discovered the relative phase does not affect the structure of the Kuznetsov-Ma breather, as demonstrated,because the relative phase of the Kuznetsov-Ma breather changes during evolution. We plot the relative phase variation with z forbreathers of the different initial states. However, altering the relative phase can cause a change in the distribution of solitons andeven the type of solitons, resulting in a diverse range of soliton forms. For example, it is converted from an anti-dark soliton toa non-rational W-shaped soliton. Because solitons usually have constant relative phases independent of the propagation distance.