no,
An auxiliary verb is also called a "helping verb" and it is always used WITH another verb.
"be" and "have" are auxiliary verbs.
Modal verbs are also auxiliary verbs.
Some modal verbs are: would, could, should, will, may, can
For example:
I AM going to the store.
He WAS eating the cake.
We HAVE been here before.
I HAVE to go now.
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A linking verb is also called "Copula" which basically means "link" in latin. A copula is usually a verb, but can also be a part of speech. A copula links the subject of the sentence with the predicate.
Some examples are:
to be, to become, to get, to feel, to seem
I AM happy.
He will BECOME a great doctor.
She FEELS tired.
He SEEMS lonely.
Sometimes, copula's can be auxiliary verbs too.
I AM feeling happy.
"am" is both a helping (auxiliary) verb and a copula here.
Source(s):
I teach English. You can also check it on Wikipedia.
