Is there any difference between 'career aspirations' and 'career goals'?
If these two are almost the same, which one is better when writing an essay?
Assuming that graduate application means applying for a higher degree in an academic institution, each can make sense depending on what you really have:
Aspirations - If you can paint this long-term vision of how getting this degree will change your life because then you'll be able to do X,Y, and Z then this would be an aspiration. Eliminating world hunger would be an example here of a big picture idea. I want there to be world peace would be another example often heard at beauty pageants.
Goal - If you can give a much more specific idea of what you plan to do after completing the program that would reflect well upon the institution. Eliminating hunger in your city by following the plans outlined in a proposal would be an example here that is fairly localized specific and would be done over the short-term. I want to end bullying in this school would be another example where the key is how specific is the objective.