I'm not completely sure whether this gives the meaning you expect, but your groups fit into the two lexical aspects of verbs, stative(static) and fientive(dynamic).
Fientive verbs are actions that occur throught a period of time, however small.
I ran home
I am about to swim a race
In contrast, stative verbs show a state of being something that is often reached at one point, even though it may continue to be a state for a period of time.
I understand what you say.
He always survives the challenge.
However, when talking about the entrance or the beginning of a state, the verb is called an inchoative or inceptive verb. This is usually found in the simple past tense, but not always.
Michael understood what she was saying.
However, some verbs can be both stative and fientive. The aspect of these verbs are then to be decided by context.
She plays the flute every Saturday.
She plays the flute.
The first sentence tells how she plays the flute on a weekly basis. In this case, plays is a fientive verb.
However the second, tells how she plays the flute, not constantly, but she has the ability to. The use of English here, turns plays into a stative verb.
So, Group A would be fientive or dynamic verbs, and Group B would be stative or static verbs.
Stative/Static verbs :http://en.wikipedia.org/wiki/Stative_verb
Fientive/Dynamic verbs :http://en.wikipedia.org/wiki/Dynamic_verb