In a previous lesson you've learned that you can use the て-form + いる to describe a current and ongoing state or situation.
In these sentences, the focus is on the current state. There is no information about how we got to the current state. In the example sentences, the て-form + いる is used in combination with the intransitive verbs 開く and 閉まる, thereby placing no focus on the actor who performed the action of opening or closing. The door might have closed "by itself", due to gravity or the wind for example.
If we want to describe a state that has come about as a result of someone's intentional action, we can use the て-form + ある instead of the て-form + いる.
Though て-form + ある describes an ongoing state that came about through a deliberate action, the focus is not on the action itself or on who did it, but on the resultant ongoing state. Who exactly performed the action is often unimportant or unknown.
The て-form + ある is mostly used with transitive verbs, which are verbs that take objects. However, note that int he construction て-form + ある, the thing that was acted upon usually isn't followed by the direct object particle を, but is usually followed either by the topic particle は, for example when the subject is already known or has been mentioned before, or to contrast the subject with other possible subjects, or by the subject particle が, for example when the subject is unknown and is being introduced for the first time, or when the speaker wants to emphasize the subject.