how many types of verbs are there, like there is action verb, any other kind?

action verbs

linking verbs

Those are the two categories into which all verbs fit.

In addition, verbs can be in any of the following

active or passive voice
indicative, interrogative, imperative, or subjunctive mood
present, past, future tenses

http://grammar.ccc.commnet.edu/grammar/verbs.htm
This is an excellent collection of terminology and explanations and examples of all the forms verbs can take.

Some verbs are used as helping verbs.

We have seen that movie.

She might have been wrong.

Yes, apart from action verbs, there are other types of verbs as well. Verbs can be classified into several categories based on their functions and characteristics. Here are some common types of verbs:

1. Action Verbs: These verbs express a physical or mental action that a subject performs, such as "run," "think," or "eat."

2. Linking Verbs: These verbs connect the subject of a sentence to a word or phrase that describes or renames it. Examples include "is," "become," or "seem."

3. Auxiliary Verbs: Also known as helping verbs, these verbs work together with main verbs to express various tenses, moods, or voice. Examples include "have," "do," or "can."

4. Modal Verbs: These verbs indicate possibility, necessity, ability, permission, or obligation. Common modal verbs include "could," "should," "can," and "must."

5. Transitive Verbs: These verbs require an object to complete their meaning. For example, in the sentence "She ate an apple," "ate" is a transitive verb, and "an apple" is its direct object.

6. Intransitive Verbs: These verbs do not require an object to complete their meaning. For instance, in the sentence "He laughed," "laughed" is an intransitive verb.

7. Regular Verbs: These verbs follow a predictable pattern when forming their past tense and past participle forms by adding "-ed" or "-d" at the end. For example, "walked," "talked," or "played."

8. Irregular Verbs: These verbs do not follow the typical pattern when forming their past tense and past participle forms. Examples include "go" (went, gone), "eat" (ate, eaten), or "run" (ran, run).

It is important to note that the classification of verbs can vary depending on different grammatical frameworks, and there may be additional subcategories within each type.