I assume you are referring to primary sources, since this was posted under "history," and that you are doing some sort of document analysis activity. In most contexts, "motive" and "purpose" are basically synonymous. However, it may be that in this case, "motive" would be appropriate to describe an author's intent in writing the document, where "purpose" might describe the purpose of the document itself. So if you were evaluating, say, a speech condemning slavery from the mid-nineteenth century, it might be useful to know that the motive of the speaker was to urge senators to vote against the Compromise of 1850. Understanding this motive might help explain things like tone, the nature of the argument, and so on. "Purpose," on the other hand, might refer to something closer to the type of document. If you were reading court records, for example, it might be useful to know that you were reading an indictment, the purpose of which was to bring charges against someone. These are really insignificant differences, though. The important thing to understand is that understanding the motive of the person who produced the document or the purpose of the document itself helps you to understand the biases within the document. Please see the link below for more information about primary sources.