Consider the following definition
Transient States
It is often useful to talk about whether a process entering a state will ever return to this state. Here is one possibility.
A state is said to be a transient state if, upon entering this state, the process may never return to this state again.
Therefore, state $i$ is transient if and only if there exists a state $j$ $( j \neq i)$ that is accessible from state $i$ but not vice versa, that is, state $i$ is not accessible from state $j$.
Thus, if state $i$ is transient and the process visits this state, there is a positive probability (perhaps even a probability of 1) that the process will later move to state $j$ and so will never return to state $i.$
Consequently, a transient state will be visited only a finite number of times.
How is it that all 1., 2. and 3. are the same?
As far as I understand they are different except the later in case 1. which I think is the same as 2.
In 1. there is the posibility of visit a state $i$ and return to this or not to return to this. If the later, then is equivalent to case 2.
In 2. there is no chance to return to $i$ never.
In 3. there is the choice to return to $i$ and then never come back to $i$.