$t'$ in time dilation formula 
in the time dilation formula, I know that $t$  is the time measured by the stationary observer between 2 events.
However, is $t'$:

*

*the time measured by the moving observer on his own clock between the 2 events,

or


*the time measured, in the frame of the observer at rest, between the moving observer starting and stopping his clock.

I feel like although the moving observer sees the light travel a greater distance at the same speed, the time interval between each tick of his clock is also increased by the same factor so the time intervals measured by each observer must be same and $t'$ should be $2$.
However, wouldn't that allow the moving observer to define the time interval, in his own frame, as 2 different things: number of ticks on his clock (same as the observer at rest) and $\text{distance}/c$ (greater than the observer at rest.
 A: In time dilation formula, $t$ is time between two events measured in frame S and $t'$ is time between the same two events measured in frame $S'.$
In the derivation of dilation formula, one usually takes time $t$ to be the time as measured by the observer B in your picture. This is the time of one tick of B's clocks in the rest frame of the clock.
Then you look at the same two events that demarcate the tick on B's clocks from the A's perspective. The A sees that between the two events $t'$ of time elapsed. So $t'$ is the time of one tick of B's clocks in the A's frame.
So if you know that one tick of B's clock took $t$ in B's frame, the dilation formula tells you for A the elapsed time of this tick is $t'=\gamma t.$
A: One is the time as measured by the stationary observer, $t$. The other is the time as measured by the moving observer, $t'$.
For the stationary observer the travelled distance is longer, $d$, than for the moving observer, $d'$. But the speed of light is same, $c$, for both. With a different observed distance but same speed the observed time must be different as well to justify the formula of $\text{speed}=\frac{\text{distance}}{\text{time}}$:
$$\text{Stationary: }\quad c=\frac dt\qquad,\qquad\text{ Moving:}\quad c=\frac{d'}{t'}$$
where $d>d'$ and $t>t'$.
So,


*

*the time measured by the moving observer on his own clock between the 2 events


is correct, yes, whereas



*the time measured, in the frame of the observer at rest, between the moving observer starting and stopping his clock


would be no different than $t$ because this is measured by the stationary observer.
