what type of word would used to define having achieved a state?

Question

... or more specifically is there a particular name for a verb in the past tense? for example the train has arrived, whereas the process of achieving the state would be to arrive

Answer 1

"Has arrived" is simply an example of the present perfect tense. If that's not what you were after, you'll need to clarify your question a bit.

Answer 2

I think you're talking about the past participle. Example: to learn -> learned, to break -> broken.