Action verbs are typically single words that describe what a person or thing in a sentence does. ( run, walk, eat, hire ) The action verb answers the question, "What is the subject doing?"
"Scott goes to work by train." The subject is Scott. Ask yourself, What is Scott doing? Scott goes so the action verb is goes.
Linking verbs are verbs that link the subject of the sentence with more information about the same subject.
"Scott is an English teacher." The word is is a linking verb because it says what Scott is.
Action verbs express a specific movement, task, act, or motion, while linking verbs express a state of being.
Some words can be both action and linking verbs.
"Freshly baked pizza smells wonderful!" Here smells is a linking verb talking about the pizza.
"I always smell grilling yakitori when I walk to the station." Here smell is an action verb talking about what I am doing.
I hope that helps you out!