Good question! Most people do not distinguish between the two, this is a big no-no.
Simply put, the complexity of the algorithm is the running time of the algorithm. This can be represented in many ways: big O, big aunt, or any of the various Landau Notations . There are also other representations, but most often used in the notes of large O, which can be used to analyze the worst time complexity of the algorithm depending on the size of the input.
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