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What's the difference between the tension and acceleration produced by a fixed pulley and movable pulley?

Is there some difference between the direction and magnitude of the tension produced by the two pulleys or is it just a difference in the acceleration acting upon the pulleys.

I came across this similar question, Free body diagram of pulley , but this only talks about tension and not the acceleration produced by the tension in the string attached to the two types of pulleys.

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