A very simple answer - 'But' joins two sentences into one sentence: "I love you, but I can't marry you." 'However" shows that a sentence is in contrast to the previous sentence: "I love you. However, I cannot marry you." There are other usages of both words, but I think those are the most common. or There are other usages of both words. However, I think those are the most common.

What is your question?