Most current pragmatic theorists are neo-Griceans in that they adopt at least some version of his main three contributions:
a fundamental distinction of what a speaker says and what she implicates;
a set of rules or principles, derived from general principles of rationality, cooperation and/or cognition, that guide, constrain or govern human linguistic communication (there are differences among neo-Griceans on the exact nature of these principles and of pragmatic reasoning generally, as we shall see); and
a notion of communicative intention (called M(eaning)-intention by Grice) whose fulfillment consists in being recognized by the addressee.
Given these similarities, there are many differences. One important dimension involves disciplines and methodology. Following Carston (2005) there are at least three different general tendencies: those who see pragmatics, much in Grice's vein, as a philosophical project; those who concentrate on its interaction with grammar; and those who see it as an empirical psychological theory of utterance interpretation.
A second dimension has to do with the relative importance given to two models of communication. One is the coding-decoding model of Locke and Saussure, as developed in the twentieth century logic and philosophy in compositional theories of meaning and truth. The other model, which we owe mostly to Grice, also has Lockean roots, in that communication of belief from speaker to hearer lies at its center. But the mechanism of discovery is not decoding according to conventional rules, but intention-recognition and discovery based on ampliative inference. The two models are not inconsistent, and all theorists accept elements of each. The issue is their relative centrality and importance in the phenomenon of human communication with language.