Deductive and Inductive are terms which refer to the way language is presented and explained in the classroom.
In an inductive approach, the examples are given first and the rules are explained or worked out (either consciously or not) with reference to those examples. Since the early 20th century, most new language teaching methods have been inductive.
As suggested above, the term inductive covers both approaches where the rules are expected to be absorbed by the brain without the need for conscious formulation (eg the Direct Method), and approaches which take the view that cognitive involvement - ie conscious understanding and formulation of rules - is useful for learning. This latter view lies, for example, behind the PPP approach (where the teacher would set up a situation, feed in the target language, and then ask concept check questions to test the learners' understanding of form and meaning/use) and the current emphasis on the need for "noticing" and the use of techniques such as Guided Discovery.
Other Related Reading in the Notebook
Thornbury, S. 30 Language Teaching Methods, Cambridge