The main difference is what can be changed inside the model that you are studying. Basically in short run you can change only limited amount of factors. Depending on what model you have it will vary.
For example if you talk about company that decide how much they want produce you will have variable cost (usually for labor) and fixed cost (usually capital). In long run you can change both factors.
Another situation: in the model of perfect competion companies can have profits in short run, but in the long run their profit is equal to zero, since long run allows new firms to enter.
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