When used in the context of astronomy, Earth-like planets and sun-like stars are terms regularly used, but are terms that can be, at best, open to interpretation.
Textbooks cannot even agree on the terminology, with one defining Centauri A as sun-like, whilst Centauri B is sometimes deemed as such and sometimes not.
The problem with defining the terminology is the lack of knowledge of other planets and their stars; more information is coming all the time, however.
A planet that is Earth-like simply due to an abundance of water, even if there is no life there, or even if the life is methane-breathing and silicon-based, would not be considered as such.
The definitions of a sun-like star or an Earth-like planet will always be relatively broad, but with restrictions in place, such as mass, age, colour, luminosity, and location will help to identify such terminology more easily in the future.
