Are Word2Vec and Doc2Vec both distributional representation or distributed representation? I have read that distributional representation is based on distributional hypothesis that words occurring in similar context tends to have similar meanings.

Word2Vec and Doc2Vec both are modeled according to this hypothesis. But, in the original paper, even they are titled as Distributed representation of words and phrases and Distributed representation of sentences and documents. So, are these algorithms based on distributional representation or distributed representation.

How about other models such as LDA and LSA.
Effectively, Word2Vec/Doc2Vec is based on distributional hypothesis where the context for each word is its nearby words. Similarly, LSA takes the entire document as the context. Both techniques solve the word embedding problem - embed words into a continuous vector space while keeping semantically related words close together.

On the other hand, LDA isn't made to solve the same problem. They deal with a different problem called topic modeling, which is finding latent topics in a set of documents.