The question was about the differences in the new grammar vs. the traditional grammar. The answer does not address that question at all. In "traditional" grammar sentences were "parsed"; that is, they were divided into "parts of speech"-- subject, predicate, adjectives, adverb, etc. Modern grammar since Noah Chomsky has used a "tree" metaphor
, in which each subject--predicate pair, called an "utterance" or a speech act," which "branch out" into "dependent (hanging) clauses." The emphasis now is the intention of the utterance, the communication function.