Are time and motion the same thing? My question might be completely irrelevant or stupid - sorry in advance if it's the case. I'm kinda lost with the time and space notions, and even formulating adequate questions is hard at that point.
But I'll give it a shot.
If time froze, the common conception would be that everything would stop moving. 
But let's do it the other way around : if everything stopped moving, would time stop? Could we consider that time still moves forward if everyting in the universe was absolutely still?
If we can make no distinction between "times stops thus nothings moves" or "nothing moves thus time stops", then isn't it some kind of a clue that time and motion and the very same thing?
 A: Time is dependent on events occurring.  Without events, there's nothing to assign time component to. You are asking about motion, which is of course an event, but just one of many possible ones.
Let's take, for example, the current SI definition of a second - "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom". 
Even if all motion has ceased, events such as this or nuclear decay, etc., will continue to occur. 
A: If there is no time, then there will be no motion but this does not mean that they are same. Motion depends on time.
A: Philosophers can argue ad infinitum about the meaning of time, so I don't think there is an authoritative answer to your question. However, I'm on your side. I take the view that time is a measure of change, and it would be meaningless in a frozen universe (ie one in which there was no change any sort). That said, I suspect that a universe with no change is an impossibility, so the notion is a hypothetical one.
A: Elapsed time is just a measure of how much some process has finished. If all processed in universe has stopped, then you would not have how to calibrate your time scale. Even there would be no of "you", because organic things are also just a complex set of processes. So no processes = no time = no measurer, either. But we can be happy that, such situation can't exist in reality. Even if you can reach absolute zero Kelvins temperature of system, it doesn't mean that such system stops motion of all it's particles in all ways. It does not - quantum fluctuations still remains at lowest temperature possible in nature. So it seems that movement is hard-coded into nature itself, albeit "time" concept at quantum fluctuations level has not much meaning in physics. If it would - we would know about universe startup a lot more than we know now. Maybe some day ...
A: Not so much, your reasoning is on point here, however you must take into consideration that motion is described for example by kinematics. In kinematics every physical variable ( velocity, acceleration, distance) is a function of time. 
by denoting: $$s(t)=...$$ $$v(t)=...$$ $$a(t)=...$$
we show that each of these quantities is dependent on the change of time. 
Therefore If we were to remove time from these relations we wouldn't be able to  create equations of motion, because motion is non existent without time.
if we were to go into quantum physics - then time can be thought of as fourth dimension….
So time and motion are distinct things, but they are deeply dependent on each other - that's how universe works. 
A: Your logic is faulty. Even assuming that both your statements are true they don't imply your conclusion. Two things that imply each other are not necessarily identical. 
A: Motion requires change in both space and time. So in that sense can we say that motion is space? I am more inclined to say that time and space both are constituents of motion.
A: If you include the motion of subatomic particles and the motion of light, we can't measure time without motion.
And of course we can't measure motion without time.
So whether they're different is a question that's outside of physics. If there isn't even theoretically an experiment we could do using unlimited resources that would tell the difference then it isn't a physics question.
