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I'm assuming you're referring to the word2vec models, in which case the the original paper here references the usage of the word "continuous" in the model name:
"We denote this model further as CBOW, as unlike standard bag-of-words model, it uses continuous distributed representation of the context".
Since word vectors are elements in $\mathbb{R}^n$, they ...
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I'm not an expert on question-answering natural language processing algorithms, but it is a very dynamic area of research, and you can easily Google it, to find many blog entries and papers on recent advancements in this area.
Since I don't have access to any such algorithm, let me use example of text-generating algorithm based on the, state of art, GPT-2 ...
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