Can one's PhD work be an extension of their Masters research?
Seeing your question, I guess this can vary from field to field, but the practice I've seen (engineering, neuroscience, and psychology) is that the PhD work often is an extension of the masters research. The masters work explores one facet of the research problem, and the PhD thesis explores two or three more. This is often a practical matter, as sometimes the masters is one step towards the eventual granting of a PhD.