Please forgive me if this is too simple for MO; most of my posts on anything contact-structure-related in Math Stack, other sites, have barely received answers (maybe because I'm not an expert in the area and my questions are not clear-enough).

1)What do we mean when we say two contact structures $(M,\xi); (M,\xi')$ are homotopic to each other ( as plane fields), and, 2) what is the precise meaning of Eliashberg's classification of O.T contact structures up to homotopy classes of plane fields?

For the first, naively, I would say that there is a pointwise homotopy of planes $\xi_p \rightarrow \xi'_p$, and the homotopy takes place in the ambient space M. But if this was the case, then there would only be , e.g., one class in $ \mathbb R^3 $ . Do we then consider the orientation of the planes relative to the orientation of the ambient space? This seems too complicated.

For the second, according to results by Eliashberg, the classification of overtwisted structures is equivalent to the classification of homotopy classes of plane fields. Do we mean that homotopy classes of planes coincide with contactomorphic classes of OT structures, i.e., if $(M^3, \xi )$ is overtwisted and H is a homotopy between the contact planes $\xi(p), \xi'(p)$ , then $\xi'$ is contactomorphic with $\xi$?.

Thanks for any help, refs., etc.