Geert Booij defines inherent inflection as “inflection of a word that is not required by its syntactic context” whereas by contextual inflection he understands “inflection that is required by the syntactic context in which a word occurs” (Booij 2007). He gives some examples, e.g. he argues that case markings on nouns are contextual but the present tense on the verb is inherent inflection.
It seems that inherent inflection is indeed equivalent to interpretable features in MP (understood as those features that have an effect on semantic interpretation, e.g. Adger 2003), whereas contextual inflection is equivalent to uninterpretable features.