The verbs such as have and do, which are used with ordinary verbs to make tenses, passive forms, questions and negatives are called auxiliary verbs or auxiliaries.
The verbs can, could, may, might, etc are used before ordinary verbs and express meanings such as permission, possibility etc.
The modals such as can, could, will, must, etc are termed defective verbs because some Parts are wanting in them. They have his-s in the third person singular. They have no infinitive and -ing form.
The auxiliary 'be' is used in the formation of the continuous tenses as;
He is working.
I was writing.
The auxiliary 'have' is used in the formation of the perfect tenses such as;
He has worked.
He has been working, and so on.
The auxiliary 'shall' is used in the first person and 'will' in all persons to express pure future tense as;
We will need the money on 15th,
You will see that I am right.