Is there a terminology for verbs describing the subject?

Question

Is there a terminology for verbs describing the state of an subject? For example:

He is a man
He suffers from headache
He lives in America
He loves swimming 

As compare to an action against an object:

He ate an apple 
He took away my book 

If possible, I would like to have access to a complete of verbs of both types.

Answer 1

Predicates that describe states (they're not all verbs) are called Stative predicates.
Predicates that describe actions are called Active predicates. This sense of "active" does not
contrast with the Passive construction; the active/stative distinction is semantic, not grammatical.

• He is a man - Predicate nouns are stative
• He is very tired. - Most predicate adjectives are stative
• He is in the garden. - Most phrasal predicates are stative
  (non-verbal predicates require an auxiliary verb be to carry tense.)

But there are lots of stative verbs, too:

• He owns a house in Ypsilanti. - Own is stative, though rent is active.
• He loves swimming - Mental state predicates are stative.
• He suffers from migraines - Physical state predicates are stative.
• He lives in America - Locative predicates are stative.

Though most adjectives are stative, there are some active ones; they mean 'act like X'

• He's being honest. - Honest can be active, and thus can be used in the progressive.