English grammar

I always thought that a main word is a head word in a phrase until my grammar teacher gave us a lesson which contained this piece of info:

1. Difference between Phrase, Clause and Sentence
1. Phrase:
A phrase is a group of words that work together to do one job but do not contain a subject and
a verb.
Grammarians tend to classify phrases in two different ways:
1. Five types according to their main word: Noun, Verb, Adjective, Adverb and Prepositional
Phrases.
2. Six types according to their headword: Participial, Gerund, Infinitive, Prepositional,
Absolute and Appositive Phrases.