I'm wondering about the theory behind pulley systems

[page123]

I'm just wondering if the tension between the masses, that is the tension from the string, is different between each mass in the following situations. Like is the T between m1 and m2 different from the T between m2 and m3? Is it for both situations or is the T the same all around in one of the situations? Could you explain this to me? I'm getting different answers from people.

So yeah, I'm asking this because it will help me apply general physics to my homework but it's not actually a homework question. Just trying to learn the concepts.

 

[Doc Al]

Making the usual assumptions of massless ropes and massless & frictionless pulleys:

In your first diagram there are two independent rope segments. Each will have its own tension.

In your second diagram there is a single rope segment and thus a single tension.