There are many technical terms used to describe grammar, vocabulary, etc. For example: determiner, inflection, morphology, subordinate clause, transitive verb.
Some glossaries have been compiled to help English teachers in British schools:
Glossary for the programmes of study for English [PDF]
UK Government: Department for Education
About 80 terms, for use in primary schools.*
Survey of English Usage, University College London
Includes the glossary above, with additional entries and explanations.
Grammatical terminology for schools
Linguistics Association of Great Britain
About 300 terms, for use in secondary schools.
*Apparently Michael Gove insisted on the inclusion of subjunctive.